LMFDB - Embedded newform 312.2.bt.d.115.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [312,2,Mod(19,312)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("312.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(312, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 6, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 312 = 2^{3} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	312.bt (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [56,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.49133254306$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			115.3
Character	$\chi$	$=$	312.115
Dual form			312.2.bt.d.19.3

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.25675 + 0.648526i) q^{2} +(0.500000 + 0.866025i) q^{3} +(1.15883 - 1.63007i) q^{4} +(0.513065 - 0.513065i) q^{5} +(-1.19001 - 0.764112i) q^{6} +(1.43100 - 0.383434i) q^{7} +(-0.399211 + 2.80011i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.312057 + 0.977529i) q^{10} +(1.43129 + 0.383513i) q^{11} +(1.99109 + 0.188540i) q^{12} +(0.967164 - 3.47341i) q^{13} +(-1.54973 + 1.40992i) q^{14} +(0.700859 + 0.187795i) q^{15} +(-1.31424 - 3.77793i) q^{16} +(1.08804 + 0.628178i) q^{17} +(0.0667332 - 1.41264i) q^{18} +(6.19113 - 1.65891i) q^{19} +(-0.241777 - 1.43088i) q^{20} +(1.04756 + 1.04756i) q^{21} +(-2.04749 + 0.446251i) q^{22} +(1.68941 + 2.92615i) q^{23} +(-2.62457 + 1.05433i) q^{24} +4.47353i q^{25} +(1.03712 + 4.99243i) q^{26} -1.00000 q^{27} +(1.03325 - 2.77695i) q^{28} +(-5.98829 + 3.45734i) q^{29} +(-1.00259 + 0.218515i) q^{30} +(-1.65000 + 1.65000i) q^{31} +(4.10176 + 3.89559i) q^{32} +(0.383513 + 1.43129i) q^{33} +(-1.77478 - 0.0838407i) q^{34} +(0.537467 - 0.930920i) q^{35} +(0.832266 + 1.81861i) q^{36} +(0.944898 - 3.52641i) q^{37} +(-6.70484 + 6.09994i) q^{38} +(3.49165 - 0.899118i) q^{39} +(1.23182 + 1.64146i) q^{40} +(0.503062 - 1.87745i) q^{41} +(-1.99589 - 0.637149i) q^{42} +(7.93214 + 4.57963i) q^{43} +(2.28377 - 1.88867i) q^{44} +(0.187795 + 0.700859i) q^{45} +(-4.02085 - 2.58180i) q^{46} +(2.96711 + 2.96711i) q^{47} +(2.61467 - 3.02713i) q^{48} +(-4.16145 + 2.40261i) q^{49} +(-2.90120 - 5.62210i) q^{50} +1.25636i q^{51} +(-4.54112 - 5.60163i) q^{52} -0.513310i q^{53} +(1.25675 - 0.648526i) q^{54} +(0.931112 - 0.537578i) q^{55} +(0.502390 + 4.16002i) q^{56} +(4.53222 + 4.53222i) q^{57} +(5.28359 - 8.22856i) q^{58} +(-3.60773 - 13.4642i) q^{59} +(1.11829 - 0.924827i) q^{60} +(-12.2267 - 7.05906i) q^{61} +(1.00357 - 3.14371i) q^{62} +(-0.383434 + 1.43100i) q^{63} +(-7.68126 - 2.23567i) q^{64} +(-1.28587 - 2.27830i) q^{65} +(-1.41021 - 1.55005i) q^{66} +(1.88176 - 7.02284i) q^{67} +(2.28482 - 1.04562i) q^{68} +(-1.68941 + 2.92615i) q^{69} +(-0.0717338 + 1.51849i) q^{70} +(-0.979852 - 3.65686i) q^{71} +(-2.22536 - 1.74578i) q^{72} +(-4.42114 + 4.42114i) q^{73} +(1.09947 + 5.04459i) q^{74} +(-3.87419 + 2.23676i) q^{75} +(4.47032 - 12.0143i) q^{76} +2.19522 q^{77} +(-3.80501 + 3.39439i) q^{78} +3.24902i q^{79} +(-2.61261 - 1.26403i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.585356 + 2.68573i) q^{82} +(-2.89926 - 2.89926i) q^{83} +(2.92154 - 0.493654i) q^{84} +(0.880529 - 0.235937i) q^{85} +(-12.9387 - 0.611226i) q^{86} +(-5.98829 - 3.45734i) q^{87} +(-1.64527 + 3.85467i) q^{88} +(-2.05252 - 0.549972i) q^{89} +(-0.690536 - 0.759013i) q^{90} +(0.0521823 - 5.34128i) q^{91} +(6.72756 + 0.637043i) q^{92} +(-2.25395 - 0.603943i) q^{93} +(-5.65316 - 1.80466i) q^{94} +(2.32532 - 4.02758i) q^{95} +(-1.32280 + 5.50002i) q^{96} +(1.09430 - 0.293217i) q^{97} +(3.67173 - 5.71829i) q^{98} +(-1.04778 + 1.04778i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 28 q^{3} - 12 q^{8} - 28 q^{9} - 28 q^{14} + 12 q^{16} - 8 q^{19} - 4 q^{20} + 10 q^{22} - 6 q^{24} + 34 q^{26} - 56 q^{27} - 14 q^{28} - 30 q^{32} + 56 q^{34} - 28 q^{40} + 40 q^{41} - 14 q^{42}+ \cdots + 4 q^{98}+O(q^{100}) $ 56 * q + 28 * q^3 - 12 * q^8 - 28 * q^9 - 28 * q^14 + 12 * q^16 - 8 * q^19 - 4 * q^20 + 10 * q^22 - 6 * q^24 + 34 * q^26 - 56 * q^27 - 14 * q^28 - 30 * q^32 + 56 * q^34 - 28 * q^40 + 40 * q^41 - 14 * q^42 - 44 * q^44 - 18 * q^46 - 12 * q^48 + 24 * q^49 - 72 * q^50 + 32 * q^52 - 54 * q^56 - 16 * q^57 - 16 * q^58 + 32 * q^59 - 20 * q^60 + 48 * q^65 + 20 * q^66 - 24 * q^67 - 26 * q^68 + 64 * q^70 + 6 * q^72 + 44 * q^73 - 6 * q^74 - 12 * q^75 + 6 * q^76 + 32 * q^78 - 4 * q^80 - 28 * q^81 - 30 * q^82 + 40 * q^83 + 2 * q^84 - 28 * q^86 + 126 * q^88 - 68 * q^89 - 72 * q^91 + 52 * q^92 + 34 * q^94 - 4 * q^97 + 4 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$-1$	$e\left(\frac{7}{12}\right)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.25675	+	0.648526i	−0.888654	+	0.458577i
$2$	−1.25675	+	0.648526i	−0.888654	+	0.458577i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	1.15883	−	1.63007i	0.579413	−	0.815034i
$5$	0.513065	−	0.513065i	0.229449	−	0.229449i	−0.583013	−	0.812463i	$-0.698126\pi$
$5$	0.513065	−	0.513065i	0.229449	−	0.229449i	0.812463	+	0.583013i	$0.198126\pi$
$6$	−1.19001	−	0.764112i	−0.485821	−	0.311947i
$7$	1.43100	−	0.383434i	0.540866	−	0.144925i	0.0219645	−	0.999759i	$-0.493008\pi$
$7$	1.43100	−	0.383434i	0.540866	−	0.144925i	0.518901	+	0.854834i	$0.326341\pi$
$8$	−0.399211	+	2.80011i	−0.141142	+	0.989989i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.312057	+	0.977529i	−0.0986809	+	0.309122i
$11$	1.43129	+	0.383513i	0.431550	+	0.115634i	0.468054	−	0.883700i	$-0.344955\pi$
$11$	1.43129	+	0.383513i	0.431550	+	0.115634i	−0.0365035	+	0.999334i	$0.511622\pi$
$12$	1.99109	+	0.188540i	0.574779	+	0.0544268i
$13$	0.967164	−	3.47341i	0.268243	−	0.963351i
$13$	0.967164	−	3.47341i	0.268243	−	0.963351i
$14$	−1.54973	+	1.40992i	−0.414184	+	0.376817i
$15$	0.700859	+	0.187795i	0.180961	+	0.0484884i
$16$	−1.31424	−	3.77793i	−0.328560	−	0.944483i
$17$	1.08804	+	0.628178i	0.263888	+	0.152356i	0.626107	−	0.779737i	$-0.284647\pi$
$17$	1.08804	+	0.628178i	0.263888	+	0.152356i	−0.362219	+	0.932093i	$0.617981\pi$
$18$	0.0667332	−	1.41264i	0.0157292	−	0.332962i
$19$	6.19113	−	1.65891i	1.42034	−	0.380580i	0.534737	−	0.845018i	$-0.320411\pi$
$19$	6.19113	−	1.65891i	1.42034	−	0.380580i	0.885605	+	0.464439i	$0.153744\pi$
$20$	−0.241777	−	1.43088i	−0.0540630	−	0.319955i
$21$	1.04756	+	1.04756i	0.228597	+	0.228597i
$22$	−2.04749	+	0.446251i	−0.436526	+	0.0951410i
$23$	1.68941	+	2.92615i	0.352267	+	0.610144i	0.986646	−	0.162878i	$-0.0520776\pi$
$23$	1.68941	+	2.92615i	0.352267	+	0.610144i	−0.634379	+	0.773022i	$0.718744\pi$
$24$	−2.62457	+	1.05433i	−0.535739	+	0.215214i
$25$			4.47353i			0.894706i
$26$	1.03712	+	4.99243i	0.203396	+	0.979097i
$27$	−1.00000			−0.192450
$28$	1.03325	−	2.77695i	0.195266	−	0.524795i
$29$	−5.98829	+	3.45734i	−1.11200	+	0.642012i	−0.939346	−	0.342971i	$-0.888567\pi$
$29$	−5.98829	+	3.45734i	−1.11200	+	0.642012i	−0.172651	+	0.984983i	$0.555233\pi$
$30$	−1.00259	+	0.218515i	−0.183048	+	0.0398953i
$31$	−1.65000	+	1.65000i	−0.296349	+	0.296349i	−0.839582	−	0.543233i	$-0.817200\pi$
$31$	−1.65000	+	1.65000i	−0.296349	+	0.296349i	0.543233	+	0.839582i	$0.317200\pi$
$32$	4.10176	+	3.89559i	0.725095	+	0.688649i
$33$	0.383513	+	1.43129i	0.0667611	+	0.249156i
$34$	−1.77478	−	0.0838407i	−0.304372	−	0.0143786i
$35$	0.537467	−	0.930920i	0.0908485	−	0.157354i
$36$	0.832266	+	1.81861i	0.138711	+	0.303101i
$37$	0.944898	−	3.52641i	0.155340	−	0.579738i	−0.843736	−	0.536759i	$-0.819649\pi$
$37$	0.944898	−	3.52641i	0.155340	−	0.579738i	0.999076	−	0.0429788i	$-0.0136848\pi$
$38$	−6.70484	+	6.09994i	−1.08767	+	0.989541i
$39$	3.49165	−	0.899118i	0.559111	−	0.143974i
$40$	1.23182	+	1.64146i	0.194768	+	0.259538i
$41$	0.503062	−	1.87745i	0.0785651	−	0.293209i	−0.915453	−	0.402425i	$-0.868167\pi$
$41$	0.503062	−	1.87745i	0.0785651	−	0.293209i	0.994018	+	0.109216i	$0.0348341\pi$
$42$	−1.99589	−	0.637149i	−0.307973	−	0.0983142i
$43$	7.93214	+	4.57963i	1.20964	+	0.698386i	0.962681	−	0.270639i	$-0.0872351\pi$
$43$	7.93214	+	4.57963i	1.20964	+	0.698386i	0.246960	+	0.969026i	$0.420568\pi$
$44$	2.28377	−	1.88867i	0.344291	−	0.284728i
$45$	0.187795	+	0.700859i	0.0279948	+	0.104478i
$46$	−4.02085	−	2.58180i	−0.592842	−	0.380666i
$47$	2.96711	+	2.96711i	0.432797	+	0.432797i	0.889579	−	0.456781i	$-0.150998\pi$
$47$	2.96711	+	2.96711i	0.432797	+	0.432797i	−0.456781	+	0.889579i	$0.650998\pi$
$48$	2.61467	−	3.02713i	0.377394	−	0.436929i
$49$	−4.16145	+	2.40261i	−0.594493	+	0.343231i
$50$	−2.90120	−	5.62210i	−0.410292	−	0.795084i
$51$			1.25636i			0.175925i
$52$	−4.54112	−	5.60163i	−0.629740	−	0.776806i
$53$		−	0.513310i		−	0.0705086i	−0.999378	−	0.0352543i	$-0.988776\pi$
$53$		−	0.513310i		−	0.0705086i	0.999378	−	0.0352543i	$-0.0112241\pi$
$54$	1.25675	−	0.648526i	0.171022	−	0.0882533i
$55$	0.931112	−	0.537578i	0.125551	−	0.0724869i
$56$	0.502390	+	4.16002i	0.0671347	+	0.555906i
$57$	4.53222	+	4.53222i	0.600307	+	0.600307i
$58$	5.28359	−	8.22856i	0.693769	−	1.08046i
$59$	−3.60773	−	13.4642i	−0.469687	−	1.75290i	−0.640863	−	0.767655i	$-0.721423\pi$
$59$	−3.60773	−	13.4642i	−0.469687	−	1.75290i	0.171176	−	0.985241i	$-0.445243\pi$
$60$	1.11829	−	0.924827i	0.144371	−	0.119395i
$61$	−12.2267	−	7.05906i	−1.56546	−	0.903820i	−0.996687	−	0.0813276i	$-0.974084\pi$
$61$	−12.2267	−	7.05906i	−1.56546	−	0.903820i	−0.568775	−	0.822493i	$-0.692583\pi$
$62$	1.00357	−	3.14371i	0.127453	−	0.399251i
$63$	−0.383434	+	1.43100i	−0.0483082	+	0.180289i
$64$	−7.68126	−	2.23567i	−0.960158	−	0.279459i
$65$	−1.28587	−	2.27830i	−0.159492	−	0.282589i
$66$	−1.41021	−	1.55005i	−0.173585	−	0.190798i
$67$	1.88176	−	7.02284i	0.229894	−	0.857977i	−0.750490	−	0.660881i	$-0.770183\pi$
$67$	1.88176	−	7.02284i	0.229894	−	0.857977i	0.980384	−	0.197095i	$-0.0631507\pi$
$68$	2.28482	−	1.04562i	0.277075	−	0.126800i
$69$	−1.68941	+	2.92615i	−0.203381	+	0.352267i
$70$	−0.0717338	+	1.51849i	−0.00857383	+	0.181495i
$71$	−0.979852	−	3.65686i	−0.116287	−	0.433989i	0.883093	−	0.469198i	$-0.155457\pi$
$71$	−0.979852	−	3.65686i	−0.116287	−	0.433989i	−0.999380	+	0.0352090i	$0.988790\pi$
$72$	−2.22536	−	1.74578i	−0.262262	−	0.205742i
$73$	−4.42114	+	4.42114i	−0.517455	+	0.517455i	−0.916801	−	0.399345i	$-0.869237\pi$
$73$	−4.42114	+	4.42114i	−0.517455	+	0.517455i	0.399345	+	0.916801i	$0.369237\pi$
$74$	1.09947	+	5.04459i	0.127811	+	0.586422i
$75$	−3.87419	+	2.23676i	−0.447353	+	0.258279i
$76$	4.47032	−	12.0143i	0.512780	−	1.37814i
$77$	2.19522			0.250169
$78$	−3.80501	+	3.39439i	−0.430833	+	0.384339i
$79$			3.24902i			0.365543i	0.983155	+	0.182771i	$0.0585068\pi$
$79$			3.24902i			0.365543i	−0.983155	+	0.182771i	$0.941493\pi$
$80$	−2.61261	−	1.26403i	−0.292099	−	0.141323i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.585356	+	2.68573i	0.0646418	+	0.296590i
$83$	−2.89926	−	2.89926i	−0.318235	−	0.318235i	0.529854	−	0.848089i	$-0.322247\pi$
$83$	−2.89926	−	2.89926i	−0.318235	−	0.318235i	−0.848089	+	0.529854i	$0.822247\pi$
$84$	2.92154	−	0.493654i	0.318766	−	0.0538620i
$85$	0.880529	−	0.235937i	0.0955068	−	0.0255910i
$86$	−12.9387	−	0.611226i	−1.39522	−	0.0659102i
$87$	−5.98829	−	3.45734i	−0.642012	−	0.370666i
$88$	−1.64527	+	3.85467i	−0.175386	+	0.410909i
$89$	−2.05252	−	0.549972i	−0.217567	−	0.0582969i	0.148389	−	0.988929i	$-0.452591\pi$
$89$	−2.05252	−	0.549972i	−0.217567	−	0.0582969i	−0.365956	+	0.930632i	$0.619258\pi$
$90$	−0.690536	−	0.759013i	−0.0727889	−	0.0800070i
$91$	0.0521823	−	5.34128i	0.00547019	−	0.559919i
$92$	6.72756	+	0.637043i	0.701396	+	0.0664163i
$93$	−2.25395	−	0.603943i	−0.233723	−	0.0626260i
$94$	−5.65316	−	1.80466i	−0.583079	−	0.186136i
$95$	2.32532	−	4.02758i	0.238573	−	0.413221i
$96$	−1.32280	+	5.50002i	−0.135008	+	0.561343i
$97$	1.09430	−	0.293217i	0.111109	−	0.0297716i	−0.202836	−	0.979213i	$-0.565016\pi$
$97$	1.09430	−	0.293217i	0.111109	−	0.0297716i	0.313945	+	0.949441i	$0.398349\pi$
$98$	3.67173	−	5.71829i	0.370901	−	0.577634i
$99$	−1.04778	+	1.04778i	−0.105306	+	0.105306i
$100$	7.29215	+	5.18405i	0.729215	+	0.518405i
$101$	−5.72724	−	9.91986i	−0.569881	−	0.987063i	−0.996577	−	0.0826680i	$-0.973656\pi$
$101$	−5.72724	−	9.91986i	−0.569881	−	0.987063i	0.426696	−	0.904395i	$-0.359677\pi$
$102$	−0.814780	−	1.57892i	−0.0806753	−	0.156337i
$103$	−2.48901			−0.245249			−0.122625	−	0.992453i	$-0.539131\pi$
$103$	−2.48901			−0.245249			−0.122625	+	0.992453i	$0.539131\pi$
$104$	9.33984	+	4.09479i	0.915847	+	0.401527i
$105$	1.07493			0.104903
$106$	0.332895	+	0.645101i	0.0323337	+	0.0626578i
$107$	−5.13018	−	8.88572i	−0.495953	−	0.859015i	0.504036	−	0.863682i	$-0.331848\pi$
$107$	−5.13018	−	8.88572i	−0.495953	−	0.859015i	−0.999989	+	0.00466706i	$0.998514\pi$
$108$	−1.15883	+	1.63007i	−0.111508	+	0.156853i
$109$	−7.21056	+	7.21056i	−0.690646	+	0.690646i	−0.962374	−	0.271728i	$-0.912405\pi$
$109$	−7.21056	+	7.21056i	−0.690646	+	0.690646i	0.271728	+	0.962374i	$0.412405\pi$
$110$	−0.821539	+	1.27945i	−0.0783306	+	0.121991i
$111$	3.52641	−	0.944898i	0.334712	−	0.0896857i
$112$	−3.32926	−	4.90228i	−0.314586	−	0.463222i
$113$	−2.37145	+	4.10748i	−0.223088	+	0.386399i	−0.955744	−	0.294200i	$-0.904947\pi$
$113$	−2.37145	+	4.10748i	−0.223088	+	0.386399i	0.732656	+	0.680599i	$0.238280\pi$
$114$	−8.63512	−	2.75659i	−0.808753	−	0.258178i
$115$	2.36808	+	0.634526i	0.220825	+	0.0591698i
$116$	−1.30369	+	13.7678i	−0.121045	+	1.27831i
$117$	2.52448	+	2.57429i	0.233388	+	0.237994i
$118$	13.2659	+	14.5814i	1.22123	+	1.34233i
$119$	1.79784	+	0.481730i	0.164808	+	0.0441601i
$120$	−0.805637	+	1.88752i	−0.0735442	+	0.172306i
$121$	−7.62477	−	4.40216i	−0.693161	−	0.400197i
$122$	19.9438	+	0.942148i	1.80563	+	0.0852981i
$123$	1.87745	−	0.503062i	0.169284	−	0.0453596i
$124$	0.777549	+	4.60169i	0.0698259	+	0.413244i
$125$	4.86053	+	4.86053i	0.434739	+	0.434739i
$126$	−0.446159	−	2.04707i	−0.0397470	−	0.182367i
$127$	9.40686	+	16.2932i	0.834724	+	1.44578i	0.894255	+	0.447558i	$0.147706\pi$
$127$	9.40686	+	16.2932i	0.834724	+	1.44578i	−0.0595311	+	0.998226i	$0.518961\pi$
$128$	11.1033	−	2.17183i	0.981402	−	0.191964i
$129$			9.15925i			0.806427i
$130$	3.09355	+	2.02933i	0.271322	+	0.177984i
$131$	−1.40105			−0.122410			−0.0612050	−	0.998125i	$-0.519494\pi$
$131$	−1.40105			−0.122410			−0.0612050	+	0.998125i	$0.519494\pi$
$132$	2.77753	+	1.03347i	0.241753	+	0.0899516i
$133$	8.22340	−	4.74778i	0.713059	−	0.411685i
$134$	2.18960	+	10.0463i	0.189152	+	0.867869i
$135$	−0.513065	+	0.513065i	−0.0441576	+	0.0441576i
$136$	−2.19333	+	2.79585i	−0.188076	+	0.239742i
$137$	−4.33906	−	16.1936i	−0.370711	−	1.38351i	−0.859511	−	0.511117i	$-0.829232\pi$
$137$	−4.33906	−	16.1936i	−0.370711	−	1.38351i	0.488800	−	0.872396i	$-0.337435\pi$
$138$	0.225480	−	4.77306i	0.0191941	−	0.406310i
$139$	−7.57593	+	13.1219i	−0.642582	+	1.11298i	0.342273	+	0.939601i	$0.388803\pi$
$139$	−7.57593	+	13.1219i	−0.642582	+	1.11298i	−0.984854	+	0.173384i	$0.944530\pi$
$140$	−0.894631	−	1.95488i	−0.0756101	−	0.165218i
$141$	−1.08604	+	4.05315i	−0.0914609	+	0.341337i
$142$	3.60299	+	3.96028i	0.302357	+	0.332340i
$143$	2.71639	−	4.60054i	0.227156	−	0.384717i
$144$	3.92891	+	0.750801i	0.327409	+	0.0625667i
$145$	−1.29854	+	4.84622i	−0.107838	+	0.402456i
$146$	2.68903	−	8.42348i	0.222546	−	0.697132i
$147$	−4.16145	−	2.40261i	−0.343231	−	0.198164i
$148$	−4.65331	−	5.62674i	−0.382499	−	0.462515i
$149$	2.01396	+	7.51621i	0.164990	+	0.615752i	0.998041	+	0.0625561i	$0.0199252\pi$
$149$	2.01396	+	7.51621i	0.164990	+	0.615752i	−0.833051	+	0.553196i	$0.813408\pi$
$150$	3.41828	−	5.32356i	0.279101	−	0.434667i
$151$	6.96070	+	6.96070i	0.566453	+	0.566453i	0.931133	−	0.364680i	$-0.118822\pi$
$151$	6.96070	+	6.96070i	0.566453	+	0.566453i	−0.364680	+	0.931133i	$0.618822\pi$
$152$	2.17357	+	17.9981i	0.176299	+	1.45984i
$153$	−1.08804	+	0.628178i	−0.0879625	+	0.0507852i
$154$	−2.75884	+	1.42366i	−0.222314	+	0.114722i
$155$			1.69312i			0.135994i
$156$	2.58059	−	6.73354i	0.206613	−	0.539115i
$157$		−	10.6185i		−	0.847450i	−0.905791	−	0.423725i	$-0.860722\pi$
$157$		−	10.6185i		−	0.847450i	0.905791	−	0.423725i	$-0.139278\pi$
$158$	−2.10707	−	4.08319i	−0.167630	−	0.324841i
$159$	0.444540	−	0.256655i	0.0352543	−	0.0203541i
$160$	4.10315	−	0.105779i	0.324383	−	0.00836255i
$161$	3.53953	+	3.53953i	0.278954	+	0.278954i
$162$	1.19001	+	0.764112i	0.0934963	+	0.0600343i
$163$	2.99986	+	11.1956i	0.234967	+	0.876908i	0.978164	+	0.207835i	$0.0666418\pi$
$163$	2.99986	+	11.1956i	0.234967	+	0.876908i	−0.743197	+	0.669073i	$0.766692\pi$
$164$	−2.47741	−	2.99567i	−0.193453	−	0.233922i
$165$	0.931112	+	0.537578i	0.0724869	+	0.0418504i
$166$	5.52388	+	1.76339i	0.428736	+	0.136866i
$167$	2.32855	−	8.69026i	0.180189	−	0.672473i	−0.815421	−	0.578868i	$-0.803494\pi$
$167$	2.32855	−	8.69026i	0.180189	−	0.672473i	0.995609	−	0.0936043i	$-0.0298389\pi$
$168$	−3.35149	+	2.51509i	−0.258573	+	0.194044i
$169$	−11.1292	−	6.71872i	−0.856091	−	0.516824i
$170$	−0.953591	+	0.867560i	−0.0731371	+	0.0665388i
$171$	−1.65891	+	6.19113i	−0.126860	+	0.473447i
$172$	16.6571	−	7.62294i	1.27009	−	0.581243i
$173$	−6.97351	+	12.0785i	−0.530186	+	0.918309i	0.469194	+	0.883095i	$0.344545\pi$
$173$	−6.97351	+	12.0785i	−0.530186	+	0.918309i	−0.999380	+	0.0352137i	$0.988789\pi$
$174$	9.76794	+	0.461439i	0.740505	+	0.0349816i
$175$	1.71530	+	6.40160i	0.129665	+	0.483916i
$176$	−0.432173	−	5.91135i	−0.0325763	−	0.445585i
$177$	9.85651	−	9.85651i	0.740861	−	0.740861i
$178$	2.93617	−	0.639940i	0.220076	−	0.0479655i
$179$	−8.03592	+	4.63954i	−0.600633	+	0.346776i	−0.769291	−	0.638899i	$-0.779390\pi$
$179$	−8.03592	+	4.63954i	−0.600633	+	0.346776i	0.168658	+	0.985675i	$0.446057\pi$
$180$	1.36007	+	0.506057i	0.101374	+	0.0377192i
$181$	20.7868			1.54507			0.772535	−	0.634973i	$-0.218989\pi$
$181$	20.7868			1.54507			0.772535	+	0.634973i	$0.218989\pi$
$182$	3.39838	+	6.74648i	0.251905	+	0.500083i
$183$		−	14.1181i		−	1.04364i
$184$	−8.86798	+	3.56240i	−0.653756	+	0.262623i
$185$	−1.32448	−	2.29407i	−0.0973778	−	0.168663i
$186$	3.22431	−	0.702740i	0.236418	−	0.0515274i
$187$	1.31638	+	1.31638i	0.0962634	+	0.0962634i
$188$	8.27496	−	1.39822i	0.603513	−	0.101976i
$189$	−1.43100	+	0.383434i	−0.104090	+	0.0278907i
$190$	−0.310353	+	6.56968i	−0.0225153	+	0.476615i
$191$	−22.5621	−	13.0262i	−1.63254	−	0.942545i	−0.983307	−	0.181952i	$-0.941759\pi$
$191$	−22.5621	−	13.0262i	−1.63254	−	0.942545i	−0.649228	−	0.760593i	$-0.724908\pi$
$192$	−1.90448	−	7.77000i	−0.137444	−	0.560752i
$193$	−14.5165	−	3.88969i	−1.04492	−	0.279986i	−0.304771	−	0.952426i	$-0.598580\pi$
$193$	−14.5165	−	3.88969i	−1.04492	−	0.279986i	−0.740152	+	0.672439i	$0.765247\pi$
$194$	−1.18510	+	1.07818i	−0.0850851	+	0.0774089i
$195$	1.33013	−	2.25275i	0.0952529	−	0.161322i
$196$	−0.905977	+	9.56766i	−0.0647126	+	0.683404i
$197$	19.2785	+	5.16566i	1.37354	+	0.368038i	0.868769	−	0.495217i	$-0.164912\pi$
$197$	19.2785	+	5.16566i	1.37354	+	0.368038i	0.504767	+	0.863255i	$0.331578\pi$
$198$	0.637280	−	1.99630i	0.0452895	−	0.141871i
$199$	−5.62998	+	9.75141i	−0.399098	+	0.691259i	−0.993615	−	0.112825i	$-0.964010\pi$
$199$	−5.62998	+	9.75141i	−0.399098	+	0.691259i	0.594516	+	0.804083i	$0.297344\pi$
$200$	−12.5264	−	1.78588i	−0.885749	−	0.126281i
$201$	7.02284	−	1.88176i	0.495353	−	0.132729i
$202$	13.6310	+	8.75250i	0.959072	+	0.615823i
$203$	−7.24355	+	7.24355i	−0.508398	+	0.508398i
$204$	2.04795	+	1.45590i	0.143385	+	0.101933i
$205$	−0.705151	−	1.22136i	−0.0492499	−	0.0853033i
$206$	3.12806	−	1.61419i	0.217942	−	0.112466i
$207$	−3.37883			−0.234845
$208$	−14.3934	+	0.911019i	−0.998003	+	0.0631678i
$209$	9.49752			0.656957
$210$	−1.35092	+	0.697123i	−0.0932223	+	0.0481061i
$211$	0.571787	+	0.990365i	0.0393635	+	0.0681795i	0.885036	−	0.465523i	$-0.154134\pi$
$211$	0.571787	+	0.990365i	0.0393635	+	0.0681795i	−0.845672	+	0.533702i	$0.820800\pi$
$212$	−0.836731	−	0.594838i	−0.0574669	−	0.0408536i
$213$	2.67700	−	2.67700i	0.183425	−	0.183425i
$214$	12.2100	+	7.84005i	0.834656	+	0.535935i
$215$	6.41935	−	1.72006i	0.437796	−	0.117307i
$216$	0.399211	−	2.80011i	0.0271628	−	0.190524i
$217$	−1.72848	+	2.99382i	−0.117337	+	0.203233i
$218$	4.38561	−	13.7381i	0.297031	−	0.930460i
$219$	−6.03939	−	1.61825i	−0.408104	−	0.109351i
$220$	0.202710	−	2.14073i	0.0136667	−	0.144328i
$221$	3.23423	−	3.17165i	0.217558	−	0.213348i
$222$	−3.81901	+	3.47447i	−0.256315	+	0.233191i
$223$	−14.1824	−	3.80017i	−0.949726	−	0.254478i	−0.249480	−	0.968380i	$-0.580260\pi$
$223$	−14.1824	−	3.80017i	−0.949726	−	0.254478i	−0.700246	+	0.713902i	$0.746926\pi$
$224$	7.36330	+	4.00181i	0.491981	+	0.267382i
$225$	−3.87419	−	2.23676i	−0.258279	−	0.149118i
$226$	0.316509	−	6.70001i	0.0210539	−	0.445678i
$227$	−8.65489	+	2.31907i	−0.574445	+	0.153922i	−0.534334	−	0.845273i	$-0.679438\pi$
$227$	−8.65489	+	2.31907i	−0.574445	+	0.153922i	−0.0401107	+	0.999195i	$0.512771\pi$
$228$	12.6399	−	2.13577i	0.837097	−	0.141445i
$229$	−1.63656	−	1.63656i	−0.108147	−	0.108147i	0.650963	−	0.759110i	$-0.274365\pi$
$229$	−1.63656	−	1.63656i	−0.108147	−	0.108147i	−0.759110	+	0.650963i	$0.774365\pi$
$230$	−3.38759	+	0.738325i	−0.223371	+	0.0486837i
$231$	1.09761	+	1.90112i	0.0722175	+	0.125084i
$232$	−7.29035	−	18.1481i	−0.478635	−	1.19148i
$233$			15.2245i			0.997391i	0.866777	+	0.498695i	$0.166187\pi$
$233$			15.2245i			0.997391i	−0.866777	+	0.498695i	$0.833813\pi$
$234$	−4.84213	−	1.59804i	−0.316540	−	0.104467i
$235$	3.04464			0.198610
$236$	−26.1284	−	9.72188i	−1.70081	−	0.632841i
$237$	−2.81373	+	1.62451i	−0.182771	+	0.105523i
$238$	−2.57185	+	0.560534i	−0.166708	+	0.0363341i
$239$	−20.1260	+	20.1260i	−1.30184	+	1.30184i	−0.374693	+	0.927149i	$0.622252\pi$
$239$	−20.1260	+	20.1260i	−1.30184	+	1.30184i	−0.927149	+	0.374693i	$0.877748\pi$
$240$	−0.211622	−	2.89461i	−0.0136601	−	0.186846i
$241$	0.968043	+	3.61278i	0.0623571	+	0.232720i	0.990070	−	0.140574i	$-0.0448949\pi$
$241$	0.968043	+	3.61278i	0.0623571	+	0.232720i	−0.927713	+	0.373294i	$0.878228\pi$
$242$	12.4373	+	0.587541i	0.799502	+	0.0377686i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−25.6753	+	11.7500i	−1.64369	+	0.752219i
$245$	−0.902396	+	3.36779i	−0.0576520	+	0.215160i
$246$	−2.03323	+	1.84980i	−0.129634	+	0.117939i
$247$	0.225764	−	23.1088i	0.0143650	−	1.47038i
$248$	−3.96150	−	5.27889i	−0.251555	−	0.335210i
$249$	1.06120	−	3.96046i	0.0672510	−	0.250984i
$250$	−9.26065	−	2.95628i	−0.585695	−	0.186971i
$251$	19.4389	+	11.2231i	1.22697	+	0.708393i	0.966395	−	0.257060i	$-0.0827538\pi$
$251$	19.4389	+	11.2231i	1.22697	+	0.708393i	0.260577	+	0.965453i	$0.416087\pi$
$252$	1.88829	+	2.28330i	0.118951	+	0.143834i
$253$	1.29582	+	4.83608i	0.0814678	+	0.304042i
$254$	−22.3886	−	14.3758i	−1.40479	−	0.902017i
$255$	0.644592	+	0.644592i	0.0403659	+	0.0403659i
$256$	−12.5455	+	9.93022i	−0.784097	+	0.620639i
$257$	25.8091	−	14.9009i	1.60993	−	0.929494i	0.620546	−	0.784170i	$-0.286911\pi$
$257$	25.8091	−	14.9009i	1.60993	−	0.929494i	0.989384	−	0.145324i	$-0.0464223\pi$
$258$	−5.94002	−	11.5109i	−0.369809	−	0.716635i
$259$		−	5.40858i		−	0.336073i
$260$	−5.20389	−	0.544108i	−0.322731	−	0.0337441i
$261$		−	6.91468i		−	0.428008i
$262$	1.76076	−	0.908616i	0.108780	−	0.0561345i
$263$	2.11644	−	1.22193i	0.130506	−	0.0753474i	−0.433326	−	0.901237i	$-0.642660\pi$
$263$	2.11644	−	1.22193i	0.130506	−	0.0753474i	0.563831	+	0.825890i	$0.309327\pi$
$264$	−4.16088	+	0.502494i	−0.256084	+	0.0309263i
$265$	−0.263361	−	0.263361i	−0.0161782	−	0.0161782i
$266$	−7.25567	+	11.2999i	−0.444874	+	0.692838i
$267$	−0.549972	−	2.05252i	−0.0336577	−	0.125612i
$268$	−9.26706	−	11.2057i	−0.566076	−	0.684495i
$269$	−22.9614	−	13.2568i	−1.39998	−	0.808280i	−0.405592	−	0.914054i	$-0.632935\pi$
$269$	−22.9614	−	13.2568i	−1.39998	−	0.808280i	−0.994390	+	0.105774i	$0.966268\pi$
$270$	0.312057	−	0.977529i	0.0189912	−	0.0594905i
$271$	−1.72024	+	6.42004i	−0.104497	+	0.389990i	−0.998288	−	0.0584956i	$-0.981370\pi$
$271$	−1.72024	+	6.42004i	−0.104497	+	0.389990i	0.893790	+	0.448485i	$0.148036\pi$
$272$	0.943273	−	4.93610i	0.0571943	−	0.299295i
$273$	4.65178	−	2.62545i	0.281538	−	0.158899i
$274$	15.9551	+	17.5373i	0.963882	+	1.05946i
$275$	−1.71566	+	6.40292i	−0.103458	+	0.386111i
$276$	2.81208	+	6.14476i	0.169268	+	0.369871i
$277$	0.878646	−	1.52186i	0.0527927	−	0.0914397i	−0.838421	−	0.545023i	$-0.816521\pi$
$277$	0.878646	−	1.52186i	0.0527927	−	0.0914397i	0.891214	+	0.453583i	$0.149854\pi$
$278$	1.01113	−	21.4041i	0.0606437	−	1.28373i
$279$	−0.603943	−	2.25395i	−0.0361571	−	0.134940i
$280$	2.39212	+	1.87660i	0.142956	+	0.112148i
$281$	17.3570	−	17.3570i	1.03543	−	1.03543i	0.0360826	−	0.999349i	$-0.488512\pi$
$281$	17.3570	−	17.3570i	1.03543	−	1.03543i	0.999349	−	0.0360826i	$-0.0114879\pi$
$282$	−1.26370	−	5.79811i	−0.0752522	−	0.345272i
$283$	−3.46233	+	1.99897i	−0.205814	+	0.118827i	−0.599364	−	0.800476i	$-0.704580\pi$
$283$	−3.46233	+	1.99897i	−0.205814	+	0.118827i	0.393551	+	0.919303i	$0.371247\pi$
$284$	−7.09640	−	2.64044i	−0.421094	−	0.156681i
$285$	4.65064			0.275480
$286$	−0.430244	+	7.54337i	−0.0254409	+	0.446049i
$287$		−	2.87952i		−	0.169973i
$288$	−5.42455	+	1.60443i	−0.319645	+	0.0945421i
$289$	−7.71078	−	13.3555i	−0.453576	−	0.785616i
$290$	−1.51096	−	6.93261i	−0.0887268	−	0.407097i
$291$	0.801083	+	0.801083i	0.0469603	+	0.0469603i
$292$	2.08342	+	12.3301i	0.121923	+	0.721564i
$293$	20.3123	−	5.44266i	1.18666	−	0.317963i	0.389093	−	0.921199i	$-0.372789\pi$
$293$	20.3123	−	5.44266i	1.18666	−	0.317963i	0.797563	+	0.603235i	$0.206122\pi$
$294$	6.78805	+	0.320668i	0.395887	+	0.0187018i
$295$	−8.75903	−	5.05703i	−0.509971	−	0.294432i
$296$	9.49712	+	4.05360i	0.552009	+	0.235611i
$297$	−1.43129	−	0.383513i	−0.0830519	−	0.0222537i
$298$	−7.40550	−	8.13987i	−0.428989	−	0.471530i
$299$	11.7977	−	3.03796i	0.682276	−	0.175690i
$300$	−0.843438	+	8.90721i	−0.0486959	+	0.514258i
$301$	13.1069	+	3.51197i	0.755466	+	0.202427i
$302$	−13.2620	−	4.23364i	−0.763144	−	0.243619i
$303$	5.72724	−	9.91986i	0.329021	−	0.569881i
$304$	−14.4039	−	21.2095i	−0.826119	−	1.21645i
$305$	−9.89482	+	2.65131i	−0.566576	+	0.151814i
$306$	0.959997	−	1.49508i	0.0548794	−	0.0854681i
$307$	−1.73231	+	1.73231i	−0.0988683	+	0.0988683i	−0.754811	−	0.655943i	$-0.772271\pi$
$307$	−1.73231	+	1.73231i	−0.0988683	+	0.0988683i	0.655943	+	0.754811i	$0.272271\pi$
$308$	2.54388	−	3.57836i	0.144951	−	0.203896i
$309$	−1.24450	−	2.15555i	−0.0707974	−	0.122625i
$310$	−1.09803	−	2.12782i	−0.0623640	−	0.120852i
$311$	−2.28061			−0.129321			−0.0646606	−	0.997907i	$-0.520596\pi$
$311$	−2.28061			−0.129321			−0.0646606	+	0.997907i	$0.520596\pi$
$312$	1.12373	+	10.1359i	0.0636186	+	0.573834i
$313$	32.2565			1.82325			0.911623	−	0.411028i	$-0.134830\pi$
$313$	32.2565			1.82325			0.911623	+	0.411028i	$0.134830\pi$
$314$	6.88639	+	13.3448i	0.388621	+	0.753090i
$315$	0.537467	+	0.930920i	0.0302828	+	0.0524514i
$316$	5.29612	+	3.76505i	0.297930	+	0.211800i
$317$	−17.9781	+	17.9781i	−1.00975	+	1.00975i	−0.00979695	+	0.999952i	$0.503119\pi$
$317$	−17.9781	+	17.9781i	−1.00975	+	1.00975i	−0.999952	+	0.00979695i	$0.996881\pi$
$318$	−0.392226	+	0.610846i	−0.0219950	+	0.0342546i
$319$	−9.89691	+	2.65187i	−0.554121	+	0.148476i
$320$	−5.08803	+	2.79394i	−0.284429	+	0.156186i
$321$	5.13018	−	8.88572i	0.286338	−	0.495953i
$322$	−6.74377	−	2.15281i	−0.375816	−	0.119972i
$323$	7.77826	+	2.08418i	0.432794	+	0.115967i
$324$	−1.99109	−	0.188540i	−0.110616	−	0.0104744i
$325$	15.5384	+	4.32664i	0.861916	+	0.239999i
$326$	−11.0307	−	12.1246i	−0.610934	−	0.671518i
$327$	−9.84980	−	2.63925i	−0.544695	−	0.145951i
$328$	5.05625	+	2.15813i	0.279185	+	0.119163i
$329$	5.38361	+	3.10823i	0.296808	+	0.171362i
$330$	−1.51881	−	0.0717486i	−0.0836075	−	0.00394963i
$331$	28.0985	−	7.52896i	1.54443	−	0.413829i	0.616736	−	0.787170i	$-0.288454\pi$
$331$	28.0985	−	7.52896i	1.54443	−	0.413829i	0.927694	+	0.373341i	$0.121788\pi$
$332$	−8.08573	+	1.36625i	−0.443762	+	0.0749826i
$333$	2.58151	+	2.58151i	0.141466	+	0.141466i
$334$	2.70947	+	12.4316i	0.148255	+	0.680226i
$335$	−2.63770	−	4.56864i	−0.144113	−	0.249611i
$336$	2.58087	−	5.33437i	0.140798	−	0.291013i
$337$		−	13.9376i		−	0.759229i	−0.925145	−	0.379615i	$-0.876057\pi$
$337$		−	13.9376i		−	0.759229i	0.925145	−	0.379615i	$-0.123943\pi$
$338$	18.3438	+	1.22616i	0.997773	+	0.0666941i
$339$	−4.74291			−0.257599
$340$	0.635787	−	1.70873i	0.0344804	−	0.0926690i
$341$	−2.99443	+	1.72884i	−0.162158	+	0.0936217i
$342$	−1.93028	−	8.85653i	−0.104378	−	0.478906i
$343$	−12.3667	+	12.3667i	−0.667739	+	0.667739i
$344$	−15.9901	+	20.3827i	−0.862126	+	1.09896i
$345$	0.634526	+	2.36808i	0.0341617	+	0.127493i
$346$	0.930729	−	19.7021i	0.0500363	−	1.05919i
$347$	−14.4501	+	25.0283i	−0.775720	+	1.34359i	0.158668	+	0.987332i	$0.449280\pi$
$347$	−14.4501	+	25.0283i	−0.775720	+	1.34359i	−0.934389	+	0.356255i	$0.884053\pi$
$348$	−12.5751	+	5.75485i	−0.674095	+	0.308493i
$349$	−5.08095	+	18.9624i	−0.271977	+	1.01503i	0.685863	+	0.727731i	$0.259425\pi$
$349$	−5.08095	+	18.9624i	−0.271977	+	1.01503i	−0.957840	+	0.287302i	$0.907242\pi$
$350$	−6.30731	−	6.93278i	−0.337140	−	0.370572i
$351$	−0.967164	+	3.47341i	−0.0516234	+	0.185397i
$352$	4.37680	+	7.14879i	0.233284	+	0.381032i
$353$	−4.83344	+	18.0387i	−0.257258	+	0.960101i	0.709562	+	0.704643i	$0.248893\pi$
$353$	−4.83344	+	18.0387i	−0.257258	+	0.960101i	−0.966820	+	0.255458i	$0.917774\pi$
$354$	−5.99494	+	18.7794i	−0.318627	+	0.998112i
$355$	−2.37893	−	1.37348i	−0.126261	−	0.0728966i
$356$	−3.27501	+	2.70843i	−0.173575	+	0.143546i
$357$	0.481730	+	1.79784i	0.0254959	+	0.0951518i
$358$	7.09026	−	11.0422i	0.374732	−	0.583600i
$359$	16.3844	+	16.3844i	0.864734	+	0.864734i	0.991884	−	0.127149i	$-0.0405827\pi$
$359$	16.3844	+	16.3844i	0.864734	+	0.864734i	−0.127149	+	0.991884i	$0.540583\pi$
$360$	−2.03745	+	0.246056i	−0.107383	+	0.0129683i
$361$	19.1236	−	11.0410i	1.00651	−	0.581107i
$362$	−26.1237	+	13.4808i	−1.37303	+	0.708534i
$363$		−	8.80433i		−	0.462107i
$364$	−8.64618	−	6.27468i	−0.453183	−	0.328883i
$365$			4.53666i			0.237460i
$366$	9.15598	+	17.7429i	0.478591	+	0.927437i
$367$	25.4992	−	14.7220i	1.33105	−	0.768480i	0.345587	−	0.938387i	$-0.387680\pi$
$367$	25.4992	−	14.7220i	1.33105	−	0.768480i	0.985460	+	0.169907i	$0.0543466\pi$
$368$	8.83450	−	10.2282i	0.460530	−	0.533179i
$369$	1.37439	+	1.37439i	0.0715479	+	0.0715479i
$370$	3.15230	+	2.02410i	0.163880	+	0.105228i
$371$	−0.196821	−	0.734545i	−0.0102184	−	0.0381357i
$372$	−3.59640	+	2.97422i	−0.186465	+	0.154206i
$373$	−20.6658	−	11.9314i	−1.07003	−	0.617785i	−0.141844	−	0.989889i	$-0.545303\pi$
$373$	−20.6658	−	11.9314i	−1.07003	−	0.617785i	−0.928191	+	0.372104i	$0.878636\pi$
$374$	−2.50807	−	0.800651i	−0.129689	−	0.0414007i
$375$	−1.77908	+	6.63961i	−0.0918712	+	0.342868i
$376$	−9.49274	+	7.12374i	−0.489551	+	0.367379i
$377$	6.21711	+	24.1436i	0.320197	+	1.24346i
$378$	1.54973	−	1.40992i	0.0797097	−	0.0725184i
$379$	3.24058	−	12.0940i	0.166457	−	0.621227i	−0.831393	−	0.555686i	$-0.812456\pi$
$379$	3.24058	−	12.0940i	0.166457	−	0.621227i	0.997850	−	0.0655416i	$-0.0208775\pi$
$380$	−3.87058	−	8.45770i	−0.198556	−	0.433871i
$381$	−9.40686	+	16.2932i	−0.481928	+	0.834724i
$382$	36.8027	+	1.73856i	1.88299	+	0.0889527i
$383$	−8.74431	−	32.6342i	−0.446814	−	1.66753i	−0.711103	−	0.703088i	$-0.751804\pi$
$383$	−8.74431	−	32.6342i	−0.446814	−	1.66753i	0.264290	−	0.964443i	$-0.414862\pi$
$384$	7.43251	+	8.52982i	0.379289	+	0.435286i
$385$	1.12629	−	1.12629i	0.0574011	−	0.0574011i
$386$	20.7662	−	4.52600i	1.05697	−	0.230367i
$387$	−7.93214	+	4.57963i	−0.403214	+	0.232795i
$388$	0.790141	−	2.12357i	0.0401133	−	0.107808i
$389$	29.5448			1.49798			0.748990	−	0.662581i	$-0.230539\pi$
$389$	29.5448			1.49798			0.748990	+	0.662581i	$0.230539\pi$
$390$	−0.210678	+	3.69376i	−0.0106681	+	0.187041i
$391$			4.24501i			0.214679i
$392$	−5.06630	−	12.6117i	−0.255887	−	0.636986i
$393$	−0.700524	−	1.21334i	−0.0353367	−	0.0612050i
$394$	−27.5783	+	6.01069i	−1.38937	+	0.302814i
$395$	1.66696	+	1.66696i	0.0838736	+	0.0838736i
$396$	0.493755	+	2.92214i	0.0248121	+	0.146843i
$397$	−28.0508	+	7.51619i	−1.40783	+	0.377227i	−0.881150	−	0.472838i	$-0.843230\pi$
$397$	−28.0508	+	7.51619i	−1.40783	+	0.377227i	−0.526679	+	0.850064i	$0.676563\pi$
$398$	0.751413	−	15.9062i	0.0376649	−	0.797308i
$399$	8.22340	+	4.74778i	0.411685	+	0.237686i
$400$	16.9007	−	5.87929i	0.845035	−	0.293965i
$401$	−5.34143	−	1.43123i	−0.266738	−	0.0714723i	0.122971	−	0.992410i	$-0.460758\pi$
$401$	−5.34143	−	1.43123i	−0.266738	−	0.0714723i	−0.389709	+	0.920938i	$0.627424\pi$
$402$	−7.60556	+	6.91940i	−0.379331	+	0.345108i
$403$	4.13532	+	7.32697i	0.205995	+	0.364982i
$404$	−22.8069	−	2.15962i	−1.13469	−	0.107445i
$405$	−0.700859	−	0.187795i	−0.0348260	−	0.00933159i
$406$	4.40568	−	13.8009i	0.218650	−	0.684930i
$407$	2.70485	−	4.68493i	0.134074	−	0.232223i
$408$	−3.51794	−	0.501551i	−0.174164	−	0.0248305i
$409$	−17.8385	+	4.77981i	−0.882056	+	0.236346i	−0.671294	−	0.741191i	$-0.734261\pi$
$409$	−17.8385	+	4.77981i	−0.882056	+	0.236346i	−0.210762	+	0.977537i	$0.567595\pi$
$410$	1.67828	+	1.07763i	0.0828843	+	0.0532203i
$411$	11.8545	−	11.8545i	0.584741	−	0.584741i
$412$	−2.88433	+	4.05725i	−0.142101	+	0.199887i
$413$	−10.3253	−	17.8840i	−0.508075	−	0.880012i
$414$	4.24633	−	2.19126i	0.208696	−	0.107694i
$415$	−2.97501			−0.146038
$416$	17.4980	−	10.4794i	0.857912	−	0.513796i
$417$	−15.1519			−0.741990
$418$	−11.9360	+	6.15939i	−0.583808	+	0.301266i
$419$	14.1415	+	24.4939i	0.690859	+	1.19660i	0.971557	+	0.236807i	$0.0761009\pi$
$419$	14.1415	+	24.4939i	0.690859	+	1.19660i	−0.280698	+	0.959796i	$0.590566\pi$
$420$	1.24566	−	1.75221i	0.0607821	−	0.0854993i
$421$	19.6915	−	19.6915i	0.959704	−	0.959704i	−0.0395149	−	0.999219i	$-0.512581\pi$
$421$	19.6915	−	19.6915i	0.959704	−	0.959704i	0.999219	+	0.0395149i	$0.0125812\pi$
$422$	−1.36087	−	0.873819i	−0.0662461	−	0.0425368i
$423$	−4.05315	+	1.08604i	−0.197071	+	0.0528050i
$424$	1.43733	+	0.204919i	0.0698028	+	0.00995174i
$425$	−2.81017	+	4.86736i	−0.136313	+	0.236102i
$426$	−1.62821	+	5.10043i	−0.0788870	+	0.247116i
$427$	−20.2030	−	5.41337i	−0.977691	−	0.261971i
$428$	−20.4293	−	1.93448i	−0.987488	−	0.0935068i
$429$	5.34238	+	0.0521930i	0.257933	+	0.00251990i
$430$	−6.95199	+	6.32479i	−0.335255	+	0.305009i
$431$	30.7854	+	8.24891i	1.48288	+	0.397336i	0.907326	−	0.420428i	$-0.138120\pi$
$431$	30.7854	+	8.24891i	1.48288	+	0.397336i	0.575553	+	0.817764i	$0.304787\pi$
$432$	1.31424	+	3.77793i	0.0632314	+	0.181766i
$433$	13.1701	+	7.60376i	0.632915	+	0.365414i	0.781880	−	0.623429i	$-0.214261\pi$
$433$	13.1701	+	7.60376i	0.632915	+	0.365414i	−0.148965	+	0.988842i	$0.547594\pi$
$434$	0.230694	−	4.88344i	0.0110737	−	0.234412i
$435$	−4.84622	+	1.29854i	−0.232358	+	0.0622602i
$436$	3.39791	+	20.1095i	0.162730	+	0.963069i
$437$	15.3136	+	15.3136i	0.732548	+	0.732548i
$438$	8.63946	−	1.88297i	0.412809	−	0.0899719i
$439$	1.65131	+	2.86016i	0.0788129	+	0.136508i	0.902738	−	0.430191i	$-0.141554\pi$
$439$	1.65131	+	2.86016i	0.0788129	+	0.136508i	−0.823925	+	0.566699i	$0.808220\pi$
$440$	1.13357	+	2.82182i	0.0540407	+	0.134525i
$441$		−	4.80523i		−	0.228820i
$442$	−2.00771	+	6.08344i	−0.0954972	+	0.289360i
$443$	−12.1161			−0.575654			−0.287827	−	0.957682i	$-0.592933\pi$
$443$	−12.1161			−0.575654			−0.287827	+	0.957682i	$0.592933\pi$
$444$	2.54625	−	6.84325i	0.120840	−	0.324766i
$445$	−1.33525	+	0.770906i	−0.0632968	+	0.0365444i
$446$	20.2882	−	4.42183i	0.960676	−	0.209380i
$447$	−5.50225	+	5.50225i	−0.260247	+	0.260247i
$448$	−11.8491	−	0.253975i	−0.559817	−	0.0119992i
$449$	2.46287	+	9.19155i	0.116230	+	0.433776i	0.999376	−	0.0353221i	$-0.0112457\pi$
$449$	2.46287	+	9.19155i	0.116230	+	0.433776i	−0.883146	+	0.469098i	$0.844579\pi$
$450$	6.31948	+	0.298533i	0.297903	+	0.0140730i
$451$	1.44006	−	2.49425i	0.0678096	−	0.117450i
$452$	3.94736	+	8.62548i	0.185668	+	0.405709i
$453$	−2.54779	+	9.50849i	−0.119706	+	0.446748i
$454$	9.37303	−	8.52741i	0.439898	−	0.400211i
$455$	−2.71365	−	2.76720i	−0.127218	−	0.129728i
$456$	−14.5000	+	10.8814i	−0.679027	+	0.509569i
$457$	−3.13824	+	11.7121i	−0.146800	+	0.547867i	0.852868	+	0.522126i	$0.174861\pi$
$457$	−3.13824	+	11.7121i	−0.146800	+	0.547867i	−0.999669	+	0.0257405i	$0.991806\pi$
$458$	3.11809	+	0.995387i	0.145699	+	0.0465114i
$459$	−1.08804	−	0.628178i	−0.0507852	−	0.0293208i
$460$	3.77852	−	3.12483i	0.176174	−	0.145696i
$461$	−6.26259	−	23.3723i	−0.291678	−	1.08856i	−0.943820	−	0.330460i	$-0.892796\pi$
$461$	−6.26259	−	23.3723i	−0.291678	−	1.08856i	0.652142	−	0.758097i	$-0.273871\pi$
$462$	−2.61235	−	1.67740i	−0.121537	−	0.0780395i
$463$	12.7547	+	12.7547i	0.592763	+	0.592763i	0.938377	−	0.345614i	$-0.112329\pi$
$463$	12.7547	+	12.7547i	0.592763	+	0.592763i	−0.345614	+	0.938377i	$0.612329\pi$
$464$	20.9316	+	18.0796i	0.971727	+	0.839323i
$465$	−1.46628	+	0.846559i	−0.0679972	+	0.0392582i
$466$	−9.87350	−	19.1334i	−0.457381	−	0.886336i
$467$		−	18.1587i		−	0.840286i	−0.907458	−	0.420143i	$-0.861980\pi$
$467$		−	18.1587i		−	0.840286i	0.907458	−	0.420143i	$-0.138020\pi$
$468$	7.12171	−	1.13191i	0.329201	−	0.0523227i
$469$		−	10.7712i		−	0.497367i
$470$	−3.82634	+	1.97453i	−0.176496	+	0.0910782i
$471$	9.19590	−	5.30926i	0.423725	−	0.244638i
$472$	39.1417	−	4.72699i	1.80164	−	0.217577i
$473$	9.59686	+	9.59686i	0.441264	+	0.441264i
$474$	2.48261	−	3.86637i	0.114030	−	0.177588i
$475$	7.42117	+	27.6962i	0.340507	+	1.27079i
$476$	2.86864	−	2.37236i	0.131484	−	0.108737i
$477$	0.444540	+	0.256655i	0.0203541	+	0.0117514i
$478$	12.2410	−	38.3455i	0.559892	−	1.75388i
$479$	4.24253	−	15.8334i	0.193846	−	0.723444i	−0.798716	−	0.601708i	$-0.794487\pi$
$479$	4.24253	−	15.8334i	0.193846	−	0.723444i	0.992562	−	0.121736i	$-0.0388463\pi$
$480$	2.14318	+	3.50055i	0.0978225	+	0.159777i
$481$	−11.3348	−	6.69263i	−0.516822	−	0.305158i
$482$	−3.55957	−	3.91256i	−0.162134	−	0.178212i
$483$	−1.29556	+	4.83509i	−0.0589499	+	0.220004i
$484$	−16.0116	+	7.32754i	−0.727800	+	0.333070i
$485$	0.411007	−	0.711885i	0.0186629	−	0.0323251i
$486$	−0.0667332	+	1.41264i	−0.00302708	+	0.0640786i
$487$	−9.33917	−	34.8542i	−0.423198	−	1.57940i	−0.767827	−	0.640658i	$-0.778662\pi$
$487$	−9.33917	−	34.8542i	−0.423198	−	1.57940i	0.344629	−	0.938739i	$-0.388005\pi$
$488$	24.6472	−	31.4180i	1.11573	−	1.42222i
$489$	−8.19576	+	8.19576i	−0.370625	+	0.370625i
$490$	−1.05002	−	4.81769i	−0.0474349	−	0.217641i
$491$	−12.9846	+	7.49664i	−0.585985	+	0.338319i	−0.763508	−	0.645798i	$-0.776525\pi$
$491$	−12.9846	+	7.49664i	−0.585985	+	0.338319i	0.177523	+	0.984117i	$0.443192\pi$
$492$	1.35562	−	3.64334i	0.0611160	−	0.164254i
$493$	−8.68730			−0.391256
$494$	14.7029	+	29.1883i	0.661516	+	1.31324i
$495$			1.07516i			0.0483246i
$496$	8.40210	+	4.06510i	0.377266	+	0.182528i
$497$	−2.80433	−	4.85724i	−0.125791	−	0.217877i
$498$	1.23480	+	5.66552i	0.0553327	+	0.253878i
$499$	−30.5157	−	30.5157i	−1.36607	−	1.36607i	−0.865965	−	0.500105i	$-0.833295\pi$
$499$	−30.5157	−	30.5157i	−1.36607	−	1.36607i	−0.500105	−	0.865965i	$-0.666705\pi$
$500$	13.5555	−	2.29048i	0.606221	−	0.102433i
$501$	8.69026	−	2.32855i	0.388252	−	0.104032i
$502$	−31.7082	−	1.49790i	−1.41521	−	0.0668546i
$503$	30.7732	+	17.7669i	1.37211	+	0.792187i	0.991193	−	0.132424i	$-0.0422760\pi$
$503$	30.7732	+	17.7669i	1.37211	+	0.792187i	0.380914	+	0.924610i	$0.375609\pi$
$504$	−3.85388	−	1.64493i	−0.171665	−	0.0732709i
$505$	−8.02797	−	2.15109i	−0.357240	−	0.0957222i
$506$	−4.76485	−	5.23736i	−0.211823	−	0.232829i
$507$	0.253986	−	12.9975i	0.0112799	−	0.577240i
$508$	37.4599	+	3.54714i	1.66201	+	0.157379i
$509$	17.3479	+	4.64835i	0.768931	+	0.206034i	0.621899	−	0.783097i	$-0.286361\pi$
$509$	17.3479	+	4.64835i	0.768931	+	0.206034i	0.147032	+	0.989132i	$0.453028\pi$
$510$	−1.22812	−	0.392054i	−0.0543822	−	0.0173605i
$511$	−4.63141	+	8.02185i	−0.204882	+	0.354866i
$512$	9.32657	−	20.6159i	0.412180	−	0.911102i
$513$	−6.19113	+	1.65891i	−0.273345	+	0.0732426i
$514$	−22.7719	+	35.4646i	−1.00443	+	1.56428i
$515$	−1.27702	+	1.27702i	−0.0562724	+	0.0562724i
$516$	14.9302	+	10.6140i	0.657265	+	0.467255i
$517$	3.10887	+	5.38472i	0.136728	+	0.236820i
$518$	3.50761	+	6.79722i	0.154115	+	0.298653i
$519$	−13.9470			−0.612206
$520$	6.89284	−	2.69105i	0.302271	−	0.118010i
$521$	−33.0188			−1.44658			−0.723289	−	0.690545i	$-0.757371\pi$
$521$	−33.0188			−1.44658			−0.723289	+	0.690545i	$0.757371\pi$
$522$	4.48435	+	8.69000i	0.196275	+	0.380351i
$523$	0.905353	+	1.56812i	0.0395883	+	0.0685690i	0.885141	−	0.465324i	$-0.154062\pi$
$523$	0.905353	+	1.56812i	0.0395883	+	0.0685690i	−0.845552	+	0.533893i	$0.820729\pi$
$524$	−1.62357	+	2.28380i	−0.0709261	+	0.0997684i
$525$	−4.68630	+	4.68630i	−0.204527	+	0.204527i
$526$	−1.86738	+	2.90823i	−0.0814217	+	0.126805i
$527$	−2.83176	+	0.758768i	−0.123353	+	0.0330524i
$528$	4.90329	−	3.32995i	0.213388	−	0.144917i
$529$	5.79177	−	10.0316i	0.251816	−	0.436158i
$530$	0.501776	+	0.160182i	0.0217957	+	0.00695786i
$531$	13.4642	+	3.60773i	0.584299	+	0.156562i
$532$	1.79029	−	18.9066i	0.0776190	−	0.819703i
$533$	−6.03462	−	3.56315i	−0.261389	−	0.154337i
$534$	2.02229	+	2.22283i	0.0875131	+	0.0961913i
$535$	−7.19106	−	1.92684i	−0.310897	−	0.0833045i
$536$	18.9135	+	8.07274i	0.816940	+	0.348689i
$537$	−8.03592	−	4.63954i	−0.346776	−	0.200211i
$538$	37.4541	+	1.76934i	1.61476	+	0.0762815i
$539$	−6.87768	+	1.84287i	−0.296243	+	0.0793780i
$540$	0.241777	+	1.43088i	0.0104044	+	0.0615754i
$541$	−27.7884	−	27.7884i	−1.19472	−	1.19472i	−0.975727	−	0.218990i	$-0.929724\pi$
$541$	−27.7884	−	27.7884i	−1.19472	−	1.19472i	−0.218990	−	0.975727i	$-0.570276\pi$
$542$	−2.00165	−	9.18399i	−0.0859783	−	0.394486i
$543$	10.3934	+	18.0019i	0.446023	+	0.772535i
$544$	2.01574	+	6.81517i	0.0864241	+	0.292198i
$545$			7.39896i			0.316937i
$546$	−4.14343	+	6.31633i	−0.177323	+	0.270314i
$547$	6.37762			0.272687			0.136344	−	0.990662i	$-0.456465\pi$
$547$	6.37762			0.272687			0.136344	+	0.990662i	$0.456465\pi$
$548$	−31.4249	−	11.6926i	−1.34240	−	0.499484i
$549$	12.2267	−	7.05906i	0.521821	−	0.301273i
$550$	−1.99632	−	9.15950i	−0.0851232	−	0.390562i
$551$	−31.3388	+	31.3388i	−1.33508	+	1.33508i
$552$	−7.51912	−	5.89870i	−0.320035	−	0.251065i
$553$	1.24578	+	4.64933i	0.0529761	+	0.197710i
$554$	−0.117270	+	2.48242i	−0.00498231	+	0.105468i
$555$	1.32448	−	2.29407i	0.0562211	−	0.0973778i
$556$	12.6104	+	27.5553i	0.534799	+	1.16860i
$557$	−1.53541	+	5.73023i	−0.0650574	+	0.242798i	−0.990795	−	0.135368i	$-0.956778\pi$
$557$	−1.53541	+	5.73023i	−0.0650574	+	0.242798i	0.925738	+	0.378166i	$0.123445\pi$
$558$	2.22075	+	2.44097i	0.0940118	+	0.103334i
$559$	23.5786	−	23.1224i	0.997269	−	0.977972i
$560$	−4.22331	−	0.807061i	−0.178468	−	0.0341046i
$561$	−0.481829	+	1.79821i	−0.0203428	+	0.0759205i
$562$	−10.5569	+	33.0698i	−0.445315	+	1.39497i
$563$	5.39506	+	3.11484i	0.227375	+	0.131275i	0.609360	−	0.792893i	$-0.291426\pi$
$563$	5.39506	+	3.11484i	0.227375	+	0.131275i	−0.381986	+	0.924168i	$0.624760\pi$
$564$	5.34837	+	6.46721i	0.225207	+	0.272319i
$565$	0.890693	+	3.32411i	0.0374717	+	0.139846i
$566$	3.05488	−	4.75761i	0.128406	−	0.199977i
$567$	−1.04756	−	1.04756i	−0.0439935	−	0.0439935i
$568$	10.6308	−	1.28384i	0.446058	−	0.0538687i
$569$	−1.68213	+	0.971181i	−0.0705187	+	0.0407140i	−0.534845	−	0.844950i	$-0.679630\pi$
$569$	−1.68213	+	0.971181i	−0.0705187	+	0.0407140i	0.464326	+	0.885664i	$0.346297\pi$
$570$	−5.84468	+	3.01607i	−0.244807	+	0.126329i
$571$		−	31.5350i		−	1.31970i	−0.751398	−	0.659850i	$-0.770620\pi$
$571$		−	31.5350i		−	1.31970i	0.751398	−	0.659850i	$-0.229380\pi$
$572$	−4.35137	−	9.75913i	−0.181940	−	0.408050i
$573$		−	26.0525i		−	1.08836i
$574$	1.86744	+	3.61883i	0.0779456	+	0.151047i
$575$	−13.0902	+	7.55764i	−0.545900	+	0.315175i
$576$	5.77678	−	5.53433i	0.240699	−	0.230597i
$577$	17.6927	+	17.6927i	0.736558	+	0.736558i	0.971910	−	0.235352i	$-0.0756242\pi$
$577$	17.6927	+	17.6927i	0.736558	+	0.736558i	−0.235352	+	0.971910i	$0.575624\pi$
$578$	18.3519	+	11.7838i	0.763338	+	0.490142i
$579$	−3.88969	−	14.5165i	−0.161650	−	0.603287i
$580$	6.39488	+	7.73263i	0.265533	+	0.321080i
$581$	−5.26050	−	3.03715i	−0.218242	−	0.126002i
$582$	−1.52628	−	0.487235i	−0.0632664	−	0.0201965i
$583$	0.196861	−	0.734696i	0.00815316	−	0.0304280i
$584$	−10.6147	−	14.1446i	−0.439240	−	0.585310i
$585$	2.61600	+	0.0255573i	0.108158	+	0.00105667i
$586$	−21.9977	+	20.0131i	−0.908716	+	0.826733i
$587$	7.64218	−	28.5210i	0.315427	−	1.17719i	−0.608165	−	0.793810i	$-0.708094\pi$
$587$	7.64218	−	28.5210i	0.315427	−	1.17719i	0.923592	−	0.383377i	$-0.125239\pi$
$588$	−8.73882	+	3.99923i	−0.360383	+	0.164925i
$589$	−7.47818	+	12.9526i	−0.308133	+	0.533702i
$590$	14.2875	+	0.674944i	0.588207	+	0.0277870i
$591$	5.16566	+	19.2785i	0.212487	+	0.793012i
$592$	−14.5643	+	1.06479i	−0.598591	+	0.0437624i
$593$	−20.5469	+	20.5469i	−0.843759	+	0.843759i	−0.989346	−	0.145586i	$-0.953493\pi$
$593$	−20.5469	+	20.5469i	−0.843759	+	0.843759i	0.145586	+	0.989346i	$0.453493\pi$
$594$	2.04749	−	0.446251i	0.0840095	−	0.0183099i
$595$	1.16957	−	0.675250i	0.0479476	−	0.0276825i
$596$	14.5858	+	5.42709i	0.597456	+	0.222302i
$597$	−11.2600			−0.460839
$598$	−12.8565	+	11.4690i	−0.525741	+	0.469004i
$599$			28.2451i			1.15407i	0.816721	+	0.577033i	$0.195789\pi$
$599$			28.2451i			1.15407i	−0.816721	+	0.577033i	$0.804211\pi$
$600$	−4.71658	−	11.7411i	−0.192553	−	0.479329i
$601$	−2.74994	−	4.76304i	−0.112172	−	0.194288i	0.804473	−	0.593989i	$-0.202448\pi$
$601$	−2.74994	−	4.76304i	−0.112172	−	0.194288i	−0.916646	+	0.399700i	$0.869114\pi$
$602$	−18.7496	+	4.08648i	−0.764177	+	0.166553i
$603$	5.14108	+	5.14108i	0.209361	+	0.209361i
$604$	19.4126	−	3.28016i	0.789889	−	0.133468i
$605$	−6.17059	+	1.65341i	−0.250870	+	0.0672205i
$606$	−0.764394	+	16.1810i	−0.0310514	+	0.657309i
$607$	−1.25794	−	0.726274i	−0.0510584	−	0.0294786i	0.474254	−	0.880388i	$-0.342718\pi$
$607$	−1.25794	−	0.726274i	−0.0510584	−	0.0294786i	−0.525312	+	0.850910i	$0.676051\pi$
$608$	31.8569	+	17.3136i	1.29197	+	0.702161i
$609$	−9.89488	−	2.65132i	−0.400961	−	0.107437i
$610$	10.7158	−	9.74908i	0.433872	−	0.394729i
$611$	13.1757	−	7.43632i	0.533031	−	0.300841i
$612$	−0.236873	+	2.50152i	−0.00957503	+	0.101118i
$613$	30.9474	+	8.29232i	1.24995	+	0.334924i	0.822318	−	0.569028i	$-0.192681\pi$
$613$	30.9474	+	8.29232i	1.24995	+	0.334924i	0.427634	+	0.903952i	$0.359347\pi$
$614$	1.05363	−	3.30053i	0.0425210	−	0.133199i
$615$	0.705151	−	1.22136i	0.0284344	−	0.0492499i
$616$	−0.876356	+	6.14687i	−0.0353094	+	0.247665i
$617$	−4.26824	+	1.14367i	−0.171833	+	0.0460425i	−0.343710	−	0.939076i	$-0.611684\pi$
$617$	−4.26824	+	1.14367i	−0.171833	+	0.0460425i	0.171877	+	0.985118i	$0.445017\pi$
$618$	2.96196	+	1.90188i	0.119147	+	0.0765049i
$619$	−8.69550	+	8.69550i	−0.349502	+	0.349502i	−0.859924	−	0.510422i	$-0.829489\pi$
$619$	−8.69550	+	8.69550i	−0.349502	+	0.349502i	0.510422	+	0.859924i	$0.329489\pi$
$620$	2.75990	+	1.96203i	0.110840	+	0.0787970i
$621$	−1.68941	−	2.92615i	−0.0677938	−	0.117422i
$622$	2.86614	−	1.47903i	0.114922	−	0.0593038i
$623$	−3.14803			−0.126123
$624$	−7.98567	−	12.0095i	−0.319683	−	0.480766i
$625$	−17.3801			−0.695204
$626$	−40.5383	+	20.9192i	−1.62024	+	0.836099i
$627$	4.74876	+	8.22509i	0.189647	+	0.328479i
$628$	−17.3089	−	12.3050i	−0.690700	−	0.491024i
$629$	3.24329	−	3.24329i	0.129319	−	0.129319i
$630$	−1.27919	−	0.821370i	−0.0509640	−	0.0327241i
$631$	−9.04870	+	2.42459i	−0.360223	+	0.0965215i	−0.434391	−	0.900724i	$-0.643037\pi$
$631$	−9.04870	+	2.42459i	−0.360223	+	0.0965215i	0.0741682	+	0.997246i	$0.476370\pi$
$632$	−9.09761	−	1.29704i	−0.361884	−	0.0515935i
$633$	−0.571787	+	0.990365i	−0.0227265	+	0.0393635i
$634$	10.9346	−	34.2531i	0.434270	−	1.36037i
$635$	13.1858	+	3.53312i	0.523261	+	0.140207i
$636$	0.0967794	−	1.02205i	0.00383755	−	0.0405269i
$637$	4.32047	+	16.7782i	0.171183	+	0.664775i
$638$	10.7181	−	9.75114i	0.424334	−	0.386051i
$639$	3.65686	+	0.979852i	0.144663	+	0.0387623i
$640$	4.58242	−	6.81100i	0.181136	−	0.269228i
$641$	−31.6965	−	18.3000i	−1.25194	−	0.722805i	−0.280442	−	0.959871i	$-0.590481\pi$
$641$	−31.6965	−	18.3000i	−1.25194	−	0.722805i	−0.971494	+	0.237066i	$0.923814\pi$
$642$	−0.684706	+	14.4942i	−0.0270232	+	0.572039i
$643$	−13.8446	+	3.70965i	−0.545977	+	0.146294i	−0.521256	−	0.853400i	$-0.674536\pi$
$643$	−13.8446	+	3.70965i	−0.545977	+	0.146294i	−0.0247210	+	0.999694i	$0.507870\pi$
$644$	9.87137	−	1.66797i	0.388987	−	0.0657272i
$645$	4.69929	+	4.69929i	0.185034	+	0.185034i
$646$	−11.1270	+	2.42512i	−0.437784	+	0.0954152i
$647$	16.5697	+	28.6996i	0.651422	+	1.12830i	0.982778	+	0.184790i	$0.0591606\pi$
$647$	16.5697	+	28.6996i	0.651422	+	1.12830i	−0.331356	+	0.943506i	$0.607506\pi$
$648$	2.62457	−	1.05433i	0.103103	−	0.0414180i
$649$		−	20.6549i		−	0.810774i
$650$	−22.3338	+	4.63958i	−0.876003	+	0.181979i
$651$	−3.45696			−0.135489
$652$	21.7259	+	8.08381i	0.850853	+	0.316586i
$653$	−35.8657	+	20.7071i	−1.40353	+	0.810330i	−0.994753	−	0.102303i	$-0.967379\pi$
$653$	−35.8657	+	20.7071i	−1.40353	+	0.810330i	−0.408780	+	0.912633i	$0.634046\pi$
$654$	14.0903	−	3.07099i	0.550976	−	0.120085i
$655$	−0.718828	+	0.718828i	−0.0280869	+	0.0280869i
$656$	−7.75403	+	0.566890i	−0.302744	+	0.0221333i
$657$	−1.61825	−	6.03939i	−0.0631339	−	0.235619i
$658$	−8.78161	−	0.414845i	−0.342343	−	0.0161723i
$659$	14.1419	−	24.4945i	0.550889	−	0.954168i	−0.447321	−	0.894373i	$-0.647622\pi$
$659$	14.1419	−	24.4945i	0.550889	−	0.954168i	0.998211	−	0.0597950i	$-0.0190447\pi$
$660$	1.95528	−	0.894815i	0.0761094	−	0.0348306i
$661$	−6.42654	+	23.9842i	−0.249963	+	0.932876i	0.720860	+	0.693081i	$0.243747\pi$
$661$	−6.42654	+	23.9842i	−0.249963	+	0.932876i	−0.970823	+	0.239796i	$0.922920\pi$
$662$	−30.4299	+	27.6846i	−1.18269	+	1.07599i
$663$	4.36384	+	1.21510i	0.169478	+	0.0471907i
$664$	9.27567	−	6.96084i	0.359966	−	0.270133i
$665$	1.78322	−	6.65505i	0.0691502	−	0.258072i
$666$	−4.91848	−	1.57013i	−0.190587	−	0.0608412i
$667$	−20.2334	−	11.6817i	−0.783440	−	0.452319i
$668$	−11.4673	−	13.8662i	−0.443684	−	0.536500i
$669$	−3.80017	−	14.1824i	−0.146923	−	0.548324i
$670$	6.27781	+	4.03100i	0.242533	+	0.155731i
$671$	−14.7927	−	14.7927i	−0.571064	−	0.571064i
$672$	0.215976	+	8.37771i	0.00833147	+	0.323177i
$673$	19.3181	−	11.1533i	0.744658	−	0.429929i	−0.0791022	−	0.996867i	$-0.525205\pi$
$673$	19.3181	−	11.1533i	0.744658	−	0.429929i	0.823761	+	0.566938i	$0.191872\pi$
$674$	9.03890	+	17.5160i	0.348165	+	0.674693i
$675$		−	4.47353i		−	0.172186i
$676$	−23.8488	+	10.3555i	−0.917260	+	0.398288i
$677$		−	7.36423i		−	0.283030i	−0.989936	−	0.141515i	$-0.954803\pi$
$677$		−	7.36423i		−	0.283030i	0.989936	−	0.141515i	$-0.0451974\pi$
$678$	5.96063	−	3.07590i	0.228917	−	0.118129i
$679$	1.45351	−	0.839184i	0.0557805	−	0.0322049i
$680$	0.309134	+	2.55977i	0.0118547	+	0.0981627i
$681$	−6.33582	−	6.33582i	−0.242789	−	0.242789i
$682$	2.64205	−	4.11468i	0.101169	−	0.157559i
$683$	1.34151	+	5.00660i	0.0513316	+	0.191572i	0.986831	−	0.161757i	$-0.0517162\pi$
$683$	1.34151	+	5.00660i	0.0513316	+	0.191572i	−0.935499	+	0.353329i	$0.885049\pi$
$684$	8.16957	+	9.87858i	0.312371	+	0.377717i
$685$	−10.5346	−	6.08214i	−0.402506	−	0.232387i
$686$	7.52169	−	23.5620i	0.287179	−	0.899600i
$687$	0.599021	−	2.23558i	0.0228541	−	0.0852926i
$688$	6.87677	−	35.9858i	0.262174	−	1.37195i
$689$	−1.78294	−	0.496455i	−0.0679245	−	0.0189134i
$690$	−2.33320	−	2.56457i	−0.0888235	−	0.0976316i
$691$	6.75090	−	25.1947i	0.256816	−	0.958451i	−0.710255	−	0.703945i	$-0.751420\pi$
$691$	6.75090	−	25.1947i	0.256816	−	0.958451i	0.967071	−	0.254506i	$-0.0819130\pi$
$692$	11.6076	+	25.3641i	0.441256	+	0.964200i
$693$	−1.09761	+	1.90112i	−0.0416948	+	0.0722175i
$694$	1.92860	−	40.8254i	0.0732086	−	1.54971i
$695$	2.84544	+	10.6193i	0.107934	+	0.402814i
$696$	12.0715	−	15.3877i	0.457570	−	0.583268i
$697$	1.72672	−	1.72672i	0.0654044	−	0.0654044i
$698$	−5.91213	−	27.1260i	−0.223777	−	1.02674i
$699$	−13.1848	+	7.61226i	−0.498695	+	0.287922i
$700$	12.4228	+	4.62229i	0.469537	+	0.174706i
$701$	−2.13901			−0.0807892			−0.0403946	−	0.999184i	$-0.512862\pi$
$701$	−2.13901			−0.0807892			−0.0403946	+	0.999184i	$0.512862\pi$
$702$	−1.03712	−	4.99243i	−0.0391436	−	0.188427i
$703$		−	23.3999i		−	0.882545i
$704$	−10.1367	−	6.14576i	−0.382042	−	0.231627i
$705$	1.52232	+	2.63673i	0.0573339	+	0.0993052i
$706$	−5.62413	−	25.8047i	−0.211667	−	0.971171i
$707$	−11.9993	−	11.9993i	−0.451279	−	0.451279i
$708$	−4.64479	−	27.4888i	−0.174562	−	1.03309i
$709$	−31.8967	+	8.54671i	−1.19791	+	0.320978i	−0.802007	−	0.597315i	$-0.796234\pi$
$709$	−31.8967	+	8.54671i	−1.19791	+	0.320978i	−0.395901	+	0.918293i	$0.629567\pi$
$710$	3.88045	+	0.183313i	0.145631	+	0.00687962i
$711$	−2.81373	−	1.62451i	−0.105523	−	0.0609238i
$712$	2.35937	−	5.52774i	0.0884212	−	0.207161i
$713$	−7.61569	−	2.04062i	−0.285210	−	0.0764218i
$714$	−1.77136	−	1.94702i	−0.0662915	−	0.0728653i
$715$	−0.966691	−	3.75406i	−0.0361522	−	0.140394i
$716$	−1.74948	+	18.4755i	−0.0653810	+	0.690462i
$717$	−27.4926	−	7.36662i	−1.02673	−	0.275112i
$718$	−31.2167	−	9.96532i	−1.16500	−	0.371902i
$719$	24.1212	−	41.7791i	0.899568	−	1.55810i	0.0715216	−	0.997439i	$-0.477215\pi$
$719$	24.1212	−	41.7791i	0.899568	−	1.55810i	0.828047	−	0.560659i	$-0.189452\pi$
$720$	2.40099	−	1.63057i	0.0894797	−	0.0607679i
$721$	−3.56176	+	0.954371i	−0.132647	+	0.0355426i
$722$	−16.8732	+	26.2780i	−0.627954	+	0.977964i
$723$	−2.64474	+	2.64474i	−0.0983590	+	0.0983590i
$724$	24.0883	−	33.8839i	0.895234	−	1.25928i
$725$	−15.4665	−	26.7888i	−0.574412	−	0.994910i
$726$	5.70984	+	11.0648i	0.211912	+	0.410654i
$727$	35.9735			1.33418			0.667092	−	0.744976i	$-0.267539\pi$
$727$	35.9735			1.33418			0.667092	+	0.744976i	$0.267539\pi$
$728$	14.9354	+	2.27841i	0.553541	+	0.0844436i
$729$	1.00000			0.0370370
$730$	−2.94214	−	5.70143i	−0.108894	−	0.211020i
$731$	5.75364	+	9.96560i	0.212806	+	0.368591i
$732$	−23.0135	−	16.3605i	−0.850603	−	0.604700i
$733$	7.99326	−	7.99326i	0.295238	−	0.295238i	−0.543907	−	0.839145i	$-0.683056\pi$
$733$	7.99326	−	7.99326i	0.295238	−	0.295238i	0.839145	+	0.543907i	$0.183056\pi$
$734$	−22.4985	+	35.0387i	−0.830433	+	1.29330i
$735$	−3.36779	+	0.902396i	−0.124223	+	0.0332854i
$736$	−4.46951	+	18.5836i	−0.164748	+	0.685001i
$737$	5.38670	−	9.33004i	0.198422	−	0.343677i
$738$	−2.61859	−	0.835933i	−0.0963916	−	0.0307711i
$739$	10.6104	+	2.84304i	0.390308	+	0.104583i	0.448636	−	0.893715i	$-0.351910\pi$
$739$	10.6104	+	2.84304i	0.390308	+	0.104583i	−0.0583274	+	0.998298i	$0.518577\pi$
$740$	−5.27433	−	0.499435i	−0.193888	−	0.0183596i
$741$	20.1257	−	11.3589i	0.739335	−	0.417279i
$742$	0.723726	+	0.795494i	0.0265688	+	0.0292035i
$743$	9.10445	+	2.43953i	0.334010	+	0.0894977i	0.421926	−	0.906630i	$-0.361354\pi$
$743$	9.10445	+	2.43953i	0.334010	+	0.0894977i	−0.0879163	+	0.996128i	$0.528021\pi$
$744$	2.59091	−	6.07020i	0.0949873	−	0.222544i
$745$	4.88959	+	2.82301i	0.179141	+	0.103427i
$746$	33.7095	+	1.59244i	1.23419	+	0.0583035i
$747$	3.96046	−	1.06120i	0.144906	−	0.0388274i
$748$	3.67125	−	0.620332i	0.134234	−	0.0226816i
$749$	−10.7484	−	10.7484i	−0.392736	−	0.392736i
$750$	−2.07011	−	9.49809i	−0.0755898	−	0.346821i
$751$	11.9625	+	20.7197i	0.436519	+	0.756073i	0.997418	−	0.0718109i	$-0.0228778\pi$
$751$	11.9625	+	20.7197i	0.436519	+	0.756073i	−0.560899	+	0.827884i	$0.689544\pi$
$752$	7.31005	−	15.1090i	0.266570	−	0.550970i
$753$			22.4461i			0.817982i
$754$	−23.4711	−	26.3104i	−0.854767	−	0.958170i
$755$	7.14257			0.259945
$756$	−1.03325	+	2.77695i	−0.0375790	+	0.100997i
$757$	4.03960	−	2.33226i	0.146822	−	0.0847676i	−0.424789	−	0.905292i	$-0.639652\pi$
$757$	4.03960	−	2.33226i	0.146822	−	0.0847676i	0.571611	+	0.820525i	$0.306319\pi$
$758$	3.77069	+	17.3007i	0.136958	+	0.628390i
$759$	−3.54026	+	3.54026i	−0.128503	+	0.128503i
$760$	10.3494	+	8.11902i	0.375411	+	0.294508i
$761$	−5.39526	−	20.1354i	−0.195578	−	0.729907i	−0.992116	−	0.125319i	$-0.960004\pi$
$761$	−5.39526	−	20.1354i	−0.195578	−	0.729907i	0.796538	−	0.604588i	$-0.206662\pi$
$762$	1.25550	−	26.5770i	0.0454820	−	0.962782i
$763$	−7.55350	+	13.0831i	−0.273455	+	0.473638i
$764$	−47.3792	+	21.6826i	−1.71412	+	0.784449i
$765$	−0.235937	+	0.880529i	−0.00853032	+	0.0318356i
$766$	32.1535	+	35.3420i	1.16175	+	1.27696i
$767$	−50.2562	−	0.490983i	−1.81464	−	0.0177284i
$768$	−14.8726	−	5.89965i	−0.536669	−	0.212885i
$769$	−10.2054	+	38.0871i	−0.368016	+	1.37346i	0.495269	+	0.868740i	$0.335070\pi$
$769$	−10.2054	+	38.0871i	−0.368016	+	1.37346i	−0.863285	+	0.504716i	$0.831597\pi$
$770$	−0.685034	+	2.14589i	−0.0246869	+	0.0773326i
$771$	25.8091	+	14.9009i	0.929494	+	0.536643i
$772$	−23.1626	+	19.1555i	−0.833641	+	0.689420i
$773$	−12.6898	−	47.3590i	−0.456421	−	1.70339i	−0.683877	−	0.729597i	$-0.739707\pi$
$773$	−12.6898	−	47.3590i	−0.456421	−	1.70339i	0.227456	−	0.973788i	$-0.426959\pi$
$774$	6.99869	−	10.8996i	0.251563	−	0.391779i
$775$	−7.38134	−	7.38134i	−0.265146	−	0.265146i
$776$	0.384184	+	3.18122i	0.0137914	+	0.114199i
$777$	4.68397	−	2.70429i	0.168036	−	0.0970158i
$778$	−37.1303	+	19.1606i	−1.33119	+	0.686940i
$779$		−	12.4581i		−	0.446357i
$780$	−2.13073	−	4.77875i	−0.0762924	−	0.171107i
$781$		−	5.60981i		−	0.200735i
$782$	−2.75300	−	5.33490i	−0.0984471	−	0.190776i
$783$	5.98829	−	3.45734i	0.214004	−	0.123555i
$784$	14.5461	+	12.5641i	0.519502	+	0.448717i
$785$	−5.44798	−	5.44798i	−0.194447	−	0.194447i
$786$	1.66727	+	1.07056i	0.0594694	+	0.0381855i
$787$	4.46886	+	16.6780i	0.159298	+	0.594507i	0.998699	+	0.0509947i	$0.0162392\pi$
$787$	4.46886	+	16.6780i	0.159298	+	0.594507i	−0.839401	+	0.543512i	$0.817094\pi$
$788$	30.7608	−	25.4392i	1.09581	−	0.906232i
$789$	2.11644	+	1.22193i	0.0753474	+	0.0435019i
$790$	−3.17601	−	1.01388i	−0.112997	−	0.0360721i
$791$	−1.81859	+	6.78708i	−0.0646617	+	0.241321i
$792$	−2.51561	−	3.35218i	−0.0893883	−	0.119114i
$793$	−36.3442	+	35.6409i	−1.29062	+	1.26565i
$794$	30.3783	−	27.6376i	1.07809	−	0.980823i
$795$	0.0963970	−	0.359758i	0.00341885	−	0.0127593i
$796$	9.37128	+	20.4774i	0.332156	+	0.725803i
$797$	−7.88369	+	13.6550i	−0.279255	+	0.483683i	−0.971200	−	0.238267i	$-0.923421\pi$
$797$	−7.88369	+	13.6550i	−0.279255	+	0.483683i	0.691945	+	0.721950i	$0.256754\pi$
$798$	−13.4138	−	0.633670i	−0.474843	−	0.0224317i
$799$	1.36445	+	5.09220i	0.0482708	+	0.180149i
$800$	−17.4270	+	18.3493i	−0.616138	+	0.648747i
$801$	1.50255	−	1.50255i	0.0530900	−	0.0530900i
$802$	7.64102	−	1.66536i	0.269814	−	0.0588060i
$803$	−8.02350	+	4.63237i	−0.283143	+	0.163473i
$804$	5.07085	−	13.6283i	0.178835	−	0.480635i
$805$	3.63201			0.128012
$806$	−9.94878	−	6.52628i	−0.350431	−	0.229878i
$807$		−	26.5136i		−	0.933322i
$808$	30.0631	−	12.0768i	1.05762	−	0.424860i
$809$	16.1331	+	27.9433i	0.567210	+	0.982436i	0.996840	+	0.0794311i	$0.0253104\pi$
$809$	16.1331	+	27.9433i	0.567210	+	0.982436i	−0.429631	+	0.903005i	$0.641356\pi$
$810$	1.00259	−	0.218515i	0.0352275	−	0.00767785i
$811$	−2.82597	−	2.82597i	−0.0992332	−	0.0992332i	0.655747	−	0.754980i	$-0.272354\pi$
$811$	−2.82597	−	2.82597i	−0.0992332	−	0.0992332i	−0.754980	+	0.655747i	$0.772354\pi$
$812$	3.41346	+	20.2015i	0.119789	+	0.708934i
$813$	−6.42004	+	1.72024i	−0.225161	+	0.0603316i
$814$	−0.361006	+	7.64194i	−0.0126533	+	0.267850i
$815$	7.28319	+	4.20495i	0.255119	+	0.147293i
$816$	4.74643	−	1.65115i	0.166158	−	0.0578020i
$817$	56.7061	+	15.1944i	1.98390	+	0.531583i
$818$	19.3186	−	17.5757i	0.675460	−	0.614521i
$819$	4.59960	+	2.71583i	0.160723	+	0.0948989i
$820$	−2.80804	−	0.265898i	−0.0980612	−	0.00928557i
$821$	25.7200	+	6.89166i	0.897635	+	0.240521i	0.678000	−	0.735062i	$-0.262847\pi$
$821$	25.7200	+	6.89166i	0.897635	+	0.240521i	0.219635	+	0.975582i	$0.429513\pi$
$822$	−7.21018	+	22.5861i	−0.251484	+	0.787782i
$823$	−1.80298	+	3.12285i	−0.0628478	+	0.108856i	−0.895737	−	0.444584i	$-0.853352\pi$
$823$	−1.80298	+	3.12285i	−0.0628478	+	0.108856i	0.832889	+	0.553439i	$0.186685\pi$
$824$	0.993639	−	6.96951i	0.0346151	−	0.242794i
$825$	−6.40292	+	1.71566i	−0.222921	+	0.0597315i
$826$	24.5745	+	15.7794i	0.855057	+	0.549035i
$827$	18.5758	−	18.5758i	0.645943	−	0.645943i	−0.306067	−	0.952010i	$-0.599013\pi$
$827$	18.5758	−	18.5758i	0.645943	−	0.645943i	0.952010	+	0.306067i	$0.0990132\pi$
$828$	−3.91547	+	5.50771i	−0.136072	+	0.191406i
$829$	0.283646	+	0.491289i	0.00985143	+	0.0170632i	0.870909	−	0.491444i	$-0.163531\pi$
$829$	0.283646	+	0.491289i	0.00985143	+	0.0170632i	−0.861058	+	0.508507i	$0.830197\pi$
$830$	3.73884	−	1.92938i	0.129777	−	0.0669696i
$831$	1.75729			0.0609598
$832$	−15.1944	+	24.5179i	−0.526772	+	0.850006i
$833$	−6.03708			−0.209172
$834$	19.0421	−	9.82638i	0.659372	−	0.340260i
$835$	−3.26397	−	5.65336i	−0.112954	−	0.195643i
$836$	11.0060	−	15.4816i	0.380650	−	0.535442i
$837$	1.65000	−	1.65000i	0.0570325	−	0.0570325i
$838$	−33.6572	−	21.6114i	−1.16267	−	0.746554i
$839$	32.7243	−	8.76844i	1.12977	−	0.302720i	0.354937	−	0.934890i	$-0.384502\pi$
$839$	32.7243	−	8.76844i	1.12977	−	0.302720i	0.774830	+	0.632170i	$0.217836\pi$
$840$	−0.429125	+	3.00994i	−0.0148062	+	0.103853i
$841$	9.40638	−	16.2923i	0.324358	−	0.561805i
$842$	−11.9768	+	37.5177i	−0.412747	+	1.29294i
$843$	23.7101	+	6.35310i	0.816619	+	0.218812i
$844$	2.27696	+	0.215609i	0.0783764	+	0.00742158i
$845$	−9.15713	+	2.26286i	−0.315015	+	0.0778446i
$846$	4.38946	−	3.99345i	0.150913	−	0.137298i
$847$	−12.5990	−	3.37588i	−0.432905	−	0.115997i
$848$	−1.93925	+	0.674613i	−0.0665942	+	0.0231663i
$849$	−3.46233	−	1.99897i	−0.118827	−	0.0686046i
$850$	0.375064	−	7.93952i	0.0128646	−	0.272323i
$851$	11.9151	−	3.19264i	0.408445	−	0.109442i
$852$	−1.26151	−	7.46588i	−0.0432187	−	0.255777i
$853$	15.4913	+	15.4913i	0.530411	+	0.530411i	0.920695	−	0.390283i	$-0.127623\pi$
$853$	15.4913	+	15.4913i	0.530411	+	0.530411i	−0.390283	+	0.920695i	$0.627623\pi$
$854$	28.9008	−	6.29893i	0.988963	−	0.215545i
$855$	2.32532	+	4.02758i	0.0795244	+	0.137740i
$856$	26.9290	−	10.8178i	0.920416	−	0.369745i
$857$			17.3171i			0.591540i	0.955259	+	0.295770i	$0.0955762\pi$
$857$			17.3171i			0.591540i	−0.955259	+	0.295770i	$0.904424\pi$
$858$	−6.74787	+	3.39908i	−0.230369	+	0.116043i
$859$	−22.9629			−0.783484			−0.391742	−	0.920075i	$-0.628127\pi$
$859$	−22.9629			−0.783484			−0.391742	+	0.920075i	$0.628127\pi$
$860$	4.63510	−	12.4572i	0.158056	−	0.424788i
$861$	2.49374	−	1.43976i	0.0849863	−	0.0490669i
$862$	−44.0391	+	9.59833i	−1.49998	+	0.326920i
$863$	−18.9344	+	18.9344i	−0.644536	+	0.644536i	−0.951667	−	0.307131i	$-0.900631\pi$
$863$	−18.9344	+	18.9344i	−0.644536	+	0.644536i	0.307131	+	0.951667i	$0.400631\pi$
$864$	−4.10176	−	3.89559i	−0.139545	−	0.132531i
$865$	2.61917	+	9.77489i	0.0890546	+	0.332356i
$866$	−21.4827	−	1.01485i	−0.730013	−	0.0344859i
$867$	7.71078	−	13.3555i	0.261872	−	0.453576i
$868$	2.87711	+	6.28686i	0.0976556	+	0.213390i
$869$	−1.24604	+	4.65029i	−0.0422690	+	0.157750i
$870$	5.24833	−	4.77484i	0.177935	−	0.161882i
$871$	−22.5732	−	13.3284i	−0.764865	−	0.451615i
$872$	−17.3118	−	23.0689i	−0.586253	−	0.781212i
$873$	−0.293217	+	1.09430i	−0.00992388	+	0.0370364i
$874$	−29.1766	−	9.31404i	−0.986912	−	0.315052i
$875$	8.81910	+	5.09171i	0.298140	+	0.172131i
$876$	−9.63646	+	7.96934i	−0.325586	+	0.269259i
$877$	11.6288	+	43.3992i	0.392676	+	1.46549i	0.825703	+	0.564106i	$0.190779\pi$
$877$	11.6288	+	43.3992i	0.392676	+	1.46549i	−0.433027	+	0.901381i	$0.642554\pi$
$878$	−3.93017	−	2.52358i	−0.132637	−	0.0851666i
$879$	14.8696	+	14.8696i	0.501540	+	0.501540i
$880$	−3.25464	−	2.81117i	−0.109714	−	0.0947645i
$881$	2.13057	−	1.23009i	0.0717808	−	0.0414427i	−0.463680	−	0.886003i	$-0.653471\pi$
$881$	2.13057	−	1.23009i	0.0717808	−	0.0414427i	0.535461	+	0.844560i	$0.320138\pi$
$882$	3.11632	+	6.03896i	0.104932	+	0.203342i
$883$			39.7470i			1.33759i	0.743446	+	0.668796i	$0.233190\pi$
$883$			39.7470i			1.33759i	−0.743446	+	0.668796i	$0.766810\pi$
$884$	−1.42209	−	8.94741i	−0.0478299	−	0.300934i
$885$		−	10.1141i		−	0.339980i
$886$	15.2269	−	7.85763i	0.511558	−	0.263982i
$887$	17.1497	−	9.90141i	0.575832	−	0.332457i	−0.183643	−	0.982993i	$-0.558789\pi$
$887$	17.1497	−	9.90141i	0.575832	−	0.332457i	0.759475	+	0.650536i	$0.225456\pi$
$888$	1.23804	+	10.2515i	0.0415459	+	0.344019i
$889$	19.7085	+	19.7085i	0.661003	+	0.661003i
$890$	1.17812	−	1.83478i	0.0394905	−	0.0615019i
$891$	−0.383513	−	1.43129i	−0.0128482	−	0.0479500i
$892$	−22.6295	+	18.7146i	−0.757692	+	0.626610i
$893$	23.2919	+	13.4476i	0.779435	+	0.450007i
$894$	3.34658	−	10.4833i	0.111926	−	0.350614i
$895$	−1.74256	+	6.50333i	−0.0582474	+	0.217382i
$896$	15.0560	−	7.36526i	0.502986	−	0.246056i
$897$	8.52978	+	8.69809i	0.284801	+	0.290421i
$898$	−9.05616	−	9.95422i	−0.302208	−	0.332177i
$899$	4.17607	−	15.5853i	0.139280	−	0.519799i
$900$	−8.13559	+	3.72317i	−0.271186	+	0.124106i
$901$	0.322450	−	0.558500i	0.0107424	−	0.0186063i
$902$	−0.192199	+	4.06855i	−0.00639953	+	0.135468i
$903$	3.51197	+	13.1069i	0.116871	+	0.436169i
$904$	−10.5547	−	8.28008i	−0.351044	−	0.275391i
$905$	10.6650	−	10.6650i	0.354515	−	0.354515i
$906$	−2.96458	−	13.6021i	−0.0984914	−	0.451899i
$907$	−16.4874	+	9.51900i	−0.547455	+	0.316073i	−0.748095	−	0.663592i	$-0.769031\pi$
$907$	−16.4874	+	9.51900i	−0.547455	+	0.316073i	0.200640	+	0.979665i	$0.435698\pi$
$908$	−6.24928	+	16.7955i	−0.207390	+	0.557377i
$909$	11.4545			0.379921
$910$	5.20497	+	1.71779i	0.172543	+	0.0569443i
$911$		−	1.28948i		−	0.0427225i	−0.999772	−	0.0213612i	$-0.993200\pi$
$911$		−	1.28948i		−	0.0427225i	0.999772	−	0.0213612i	$-0.00680001\pi$
$912$	11.1660	−	23.0789i	0.369743	−	0.764217i
$913$	−3.03778	−	5.26159i	−0.100536	−	0.174133i
$914$	−3.65161	−	16.7543i	−0.120784	−	0.554184i
$915$	−7.24351	−	7.24351i	−0.239463	−	0.239463i
$916$	−4.56418	+	0.771212i	−0.150805	+	0.0254816i
$917$	−2.00489	+	0.537210i	−0.0662074	+	0.0177402i
$918$	1.77478	+	0.0838407i	0.0585764	+	0.00276716i
$919$	23.2515	+	13.4243i	0.766997	+	0.442826i	0.831802	−	0.555072i	$-0.187309\pi$
$919$	23.2515	+	13.4243i	0.766997	+	0.442826i	−0.0648055	+	0.997898i	$0.520643\pi$
$920$	−2.72211	+	6.37759i	−0.0897452	+	0.210263i
$921$	−2.36638	−	0.634071i	−0.0779750	−	0.0208933i
$922$	23.0281	+	25.3116i	0.758389	+	0.833595i
$923$	−13.6494	−	0.133350i	−0.449277	−	0.00438926i
$924$	4.37089	+	0.413887i	0.143792	+	0.0136159i
$925$	15.7755	+	4.22703i	0.518695	+	0.138984i
$926$	−24.3013	−	7.75770i	−0.798589	−	0.254934i
$927$	1.24450	−	2.15555i	0.0408749	−	0.0707974i
$928$	−38.0309	−	9.14672i	−1.24842	−	0.300256i
$929$	37.8024	−	10.1291i	1.24026	−	0.332326i	0.421692	−	0.906739i	$-0.361436\pi$
$929$	37.8024	−	10.1291i	1.24026	−	0.332326i	0.818566	+	0.574413i	$0.194770\pi$
$930$	1.29373	−	2.01483i	0.0424231	−	0.0660690i
$931$	−21.7784	+	21.7784i	−0.713757	+	0.713757i
$932$	24.8170	+	17.6426i	0.812907	+	0.577902i
$933$	−1.14030	−	1.97506i	−0.0373318	−	0.0646606i
$934$	11.7764	+	22.8209i	0.385336	+	0.746724i
$935$	1.35078			0.0441752
$936$	−8.21611	+	6.04115i	−0.268552	+	0.197461i
$937$	46.1571			1.50789			0.753943	−	0.656939i	$-0.228149\pi$
$937$	46.1571			1.50789			0.753943	+	0.656939i	$0.228149\pi$
$938$	6.98540	+	13.5367i	0.228081	+	0.441988i
$939$	16.1283	+	27.9350i	0.526326	+	0.911623i
$940$	3.52821	−	4.96297i	0.115077	−	0.161874i
$941$	35.7367	−	35.7367i	1.16498	−	1.16498i	0.181611	−	0.983370i	$-0.441869\pi$
$941$	35.7367	−	35.7367i	1.16498	−	1.16498i	0.983370	−	0.181611i	$-0.0581313\pi$
$942$	−8.11373	+	12.6362i	−0.264360	+	0.411709i
$943$	6.34359	−	1.69976i	0.206576	−	0.0553518i
$944$	−46.1256	+	31.3250i	−1.50126	+	1.01954i
$945$	−0.537467	+	0.930920i	−0.0174838	+	0.0302828i
$946$	−18.2846	−	5.83701i	−0.594485	−	0.189777i
$947$	0.723796	+	0.193941i	0.0235202	+	0.00630222i	0.270560	−	0.962703i	$-0.412791\pi$
$947$	0.723796	+	0.193941i	0.0235202	+	0.00630222i	−0.247040	+	0.969005i	$0.579458\pi$
$948$	−0.612569	+	6.46909i	−0.0198953	+	0.210106i
$949$	11.0805	+	19.6324i	0.359687	+	0.637295i
$950$	−27.2883	−	29.9943i	−0.885348	−	0.973143i
$951$	−24.5585	−	6.58043i	−0.796364	−	0.213385i
$952$	−2.06662	+	4.84184i	−0.0669794	+	0.156925i
$953$	−41.5062	−	23.9636i	−1.34452	−	0.776257i	−0.357050	−	0.934085i	$-0.616217\pi$
$953$	−41.5062	−	23.9636i	−1.34452	−	0.776257i	−0.987467	+	0.157828i	$0.949551\pi$
$954$	−0.725122	−	0.0342549i	−0.0234767	−	0.00110904i
$955$	−18.2591	+	4.89251i	−0.590851	+	0.158318i
$956$	9.48418	+	56.1293i	0.306740	+	1.81535i
$957$	−7.24504	−	7.24504i	−0.234199	−	0.234199i
$958$	4.93656	+	22.6499i	0.159493	+	0.731786i
$959$	−12.4184	−	21.5092i	−0.401010	−	0.694569i
$960$	−4.96364	−	3.00939i	−0.160201	−	0.0971276i
$961$			25.5550i			0.824354i
$962$	18.5853	+	1.06003i	0.599215	+	0.0341769i
$963$	10.2604			0.330635
$964$	7.01088	+	2.60862i	0.225805	+	0.0840179i
$965$	−9.44359	+	5.45226i	−0.304000	+	0.175514i
$966$	−1.50749	−	6.91668i	−0.0485028	−	0.222541i
$967$	8.44481	−	8.44481i	0.271567	−	0.271567i	−0.558164	−	0.829731i	$-0.688494\pi$
$967$	8.44481	−	8.44481i	0.271567	−	0.271567i	0.829731	+	0.558164i	$0.188494\pi$
$968$	15.3704	−	19.5928i	0.494025	−	0.629737i
$969$	2.08418	+	7.77826i	0.0669535	+	0.249874i
$970$	−0.0548557	+	1.16121i	−0.00176131	+	0.0372842i
$971$	24.1539	−	41.8358i	0.775136	−	1.34257i	−0.159582	−	0.987185i	$-0.551015\pi$
$971$	24.1539	−	41.8358i	0.775136	−	1.34257i	0.934718	−	0.355390i	$-0.115652\pi$
$972$	−0.832266	−	1.81861i	−0.0266950	−	0.0583319i
$973$	−5.80974	+	21.6822i	−0.186252	+	0.695101i
$974$	34.3409	+	37.7463i	1.10035	+	1.20947i
$975$	4.02223	+	15.6200i	0.128814	+	0.500240i
$976$	−10.5999	+	55.4688i	−0.339295	+	1.77551i
$977$	8.21436	−	30.6564i	0.262801	−	0.980786i	−0.700782	−	0.713376i	$-0.747165\pi$
$977$	8.21436	−	30.6564i	0.262801	−	0.980786i	0.963583	−	0.267410i	$-0.0861679\pi$
$978$	4.98483	−	15.6152i	0.159397	−	0.499318i
$979$	−2.72683	−	1.57434i	−0.0871500	−	0.0503161i
$980$	4.44400	+	5.37365i	0.141958	+	0.171655i
$981$	−2.63925	−	9.84980i	−0.0842647	−	0.314480i
$982$	11.4565	−	17.8422i	0.365593	−	0.569368i
$983$	18.1345	+	18.1345i	0.578400	+	0.578400i	0.934462	−	0.356062i	$-0.115881\pi$
$983$	18.1345	+	18.1345i	0.578400	+	0.578400i	−0.356062	+	0.934462i	$0.615881\pi$
$984$	0.659131	+	5.45791i	0.0210123	+	0.173992i
$985$	12.5414	−	7.24080i	0.399603	−	0.230711i
$986$	10.9177	−	5.63394i	0.347692	−	0.179421i
$987$			6.21646i			0.197872i
$988$	−37.4073	−	27.1471i	−1.19008	−	0.863664i
$989$			30.9475i			0.984074i
$990$	−0.697266	−	1.35120i	−0.0221606	−	0.0429439i
$991$	15.3411	−	8.85718i	0.487326	−	0.281358i	−0.236139	−	0.971719i	$-0.575882\pi$
$991$	15.3411	−	8.85718i	0.487326	−	0.281358i	0.723464	+	0.690362i	$0.242549\pi$
$992$	−13.1956	+	0.340182i	−0.418962	+	0.0108008i
$993$	20.5695	+	20.5695i	0.652753	+	0.652753i
$994$	6.67438	+	4.28564i	0.211698	+	0.135932i
$995$	2.11456	+	7.89164i	0.0670360	+	0.250182i
$996$	−5.22607	−	6.31932i	−0.165594	−	0.200235i
$997$	4.27051	+	2.46558i	0.135249	+	0.0780858i	0.566098	−	0.824338i	$-0.308453\pi$
$997$	4.27051	+	2.46558i	0.135249	+	0.0780858i	−0.430849	+	0.902424i	$0.641786\pi$
$998$	58.1407	+	18.5603i	1.84041	+	0.587515i
$999$	−0.944898	+	3.52641i	−0.0298952	+	0.111571i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	312.2.bt.d.115.3	yes	56
3.2	odd	2		936.2.ed.e.739.12		56
8.3	odd	2	inner	312.2.bt.d.115.10	yes	56
13.6	odd	12	inner	312.2.bt.d.19.10	yes	56
24.11	even	2		936.2.ed.e.739.5		56
39.32	even	12		936.2.ed.e.19.5		56
104.19	even	12	inner	312.2.bt.d.19.3	✓	56
312.227	odd	12		936.2.ed.e.19.12		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bt.d.19.3	✓	56	104.19	even	12	inner
312.2.bt.d.19.10	yes	56	13.6	odd	12	inner
312.2.bt.d.115.3	yes	56	1.1	even	1	trivial
312.2.bt.d.115.10	yes	56	8.3	odd	2	inner
936.2.ed.e.19.5		56	39.32	even	12
936.2.ed.e.19.12		56	312.227	odd	12
936.2.ed.e.739.5		56	24.11	even	2
936.2.ed.e.739.12		56	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	312.bt (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.25675 + 0.648526i) q^{2} +(0.500000 + 0.866025i) q^{3} +(1.15883 - 1.63007i) q^{4} +(0.513065 - 0.513065i) q^{5} +(-1.19001 - 0.764112i) q^{6} +(1.43100 - 0.383434i) q^{7} +(-0.399211 + 2.80011i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.312057 + 0.977529i) q^{10} +(1.43129 + 0.383513i) q^{11} +(1.99109 + 0.188540i) q^{12} +(0.967164 - 3.47341i) q^{13} +(-1.54973 + 1.40992i) q^{14} +(0.700859 + 0.187795i) q^{15} +(-1.31424 - 3.77793i) q^{16} +(1.08804 + 0.628178i) q^{17} +(0.0667332 - 1.41264i) q^{18} +(6.19113 - 1.65891i) q^{19} +(-0.241777 - 1.43088i) q^{20} +(1.04756 + 1.04756i) q^{21} +(-2.04749 + 0.446251i) q^{22} +(1.68941 + 2.92615i) q^{23} +(-2.62457 + 1.05433i) q^{24} +4.47353i q^{25} +(1.03712 + 4.99243i) q^{26} -1.00000 q^{27} +(1.03325 - 2.77695i) q^{28} +(-5.98829 + 3.45734i) q^{29} +(-1.00259 + 0.218515i) q^{30} +(-1.65000 + 1.65000i) q^{31} +(4.10176 + 3.89559i) q^{32} +(0.383513 + 1.43129i) q^{33} +(-1.77478 - 0.0838407i) q^{34} +(0.537467 - 0.930920i) q^{35} +(0.832266 + 1.81861i) q^{36} +(0.944898 - 3.52641i) q^{37} +(-6.70484 + 6.09994i) q^{38} +(3.49165 - 0.899118i) q^{39} +(1.23182 + 1.64146i) q^{40} +(0.503062 - 1.87745i) q^{41} +(-1.99589 - 0.637149i) q^{42} +(7.93214 + 4.57963i) q^{43} +(2.28377 - 1.88867i) q^{44} +(0.187795 + 0.700859i) q^{45} +(-4.02085 - 2.58180i) q^{46} +(2.96711 + 2.96711i) q^{47} +(2.61467 - 3.02713i) q^{48} +(-4.16145 + 2.40261i) q^{49} +(-2.90120 - 5.62210i) q^{50} +1.25636i q^{51} +(-4.54112 - 5.60163i) q^{52} -0.513310i q^{53} +(1.25675 - 0.648526i) q^{54} +(0.931112 - 0.537578i) q^{55} +(0.502390 + 4.16002i) q^{56} +(4.53222 + 4.53222i) q^{57} +(5.28359 - 8.22856i) q^{58} +(-3.60773 - 13.4642i) q^{59} +(1.11829 - 0.924827i) q^{60} +(-12.2267 - 7.05906i) q^{61} +(1.00357 - 3.14371i) q^{62} +(-0.383434 + 1.43100i) q^{63} +(-7.68126 - 2.23567i) q^{64} +(-1.28587 - 2.27830i) q^{65} +(-1.41021 - 1.55005i) q^{66} +(1.88176 - 7.02284i) q^{67} +(2.28482 - 1.04562i) q^{68} +(-1.68941 + 2.92615i) q^{69} +(-0.0717338 + 1.51849i) q^{70} +(-0.979852 - 3.65686i) q^{71} +(-2.22536 - 1.74578i) q^{72} +(-4.42114 + 4.42114i) q^{73} +(1.09947 + 5.04459i) q^{74} +(-3.87419 + 2.23676i) q^{75} +(4.47032 - 12.0143i) q^{76} +2.19522 q^{77} +(-3.80501 + 3.39439i) q^{78} +3.24902i q^{79} +(-2.61261 - 1.26403i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.585356 + 2.68573i) q^{82} +(-2.89926 - 2.89926i) q^{83} +(2.92154 - 0.493654i) q^{84} +(0.880529 - 0.235937i) q^{85} +(-12.9387 - 0.611226i) q^{86} +(-5.98829 - 3.45734i) q^{87} +(-1.64527 + 3.85467i) q^{88} +(-2.05252 - 0.549972i) q^{89} +(-0.690536 - 0.759013i) q^{90} +(0.0521823 - 5.34128i) q^{91} +(6.72756 + 0.637043i) q^{92} +(-2.25395 - 0.603943i) q^{93} +(-5.65316 - 1.80466i) q^{94} +(2.32532 - 4.02758i) q^{95} +(-1.32280 + 5.50002i) q^{96} +(1.09430 - 0.293217i) q^{97} +(3.67173 - 5.71829i) q^{98} +(-1.04778 + 1.04778i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 28 q^{3} - 12 q^{8} - 28 q^{9} - 28 q^{14} + 12 q^{16} - 8 q^{19} - 4 q^{20} + 10 q^{22} - 6 q^{24} + 34 q^{26} - 56 q^{27} - 14 q^{28} - 30 q^{32} + 56 q^{34} - 28 q^{40} + 40 q^{41} - 14 q^{42}+ \cdots + 4 q^{98}+O(q^{100}) \) 56 * q + 28 * q^3 - 12 * q^8 - 28 * q^9 - 28 * q^14 + 12 * q^16 - 8 * q^19 - 4 * q^20 + 10 * q^22 - 6 * q^24 + 34 * q^26 - 56 * q^27 - 14 * q^28 - 30 * q^32 + 56 * q^34 - 28 * q^40 + 40 * q^41 - 14 * q^42 - 44 * q^44 - 18 * q^46 - 12 * q^48 + 24 * q^49 - 72 * q^50 + 32 * q^52 - 54 * q^56 - 16 * q^57 - 16 * q^58 + 32 * q^59 - 20 * q^60 + 48 * q^65 + 20 * q^66 - 24 * q^67 - 26 * q^68 + 64 * q^70 + 6 * q^72 + 44 * q^73 - 6 * q^74 - 12 * q^75 + 6 * q^76 + 32 * q^78 - 4 * q^80 - 28 * q^81 - 30 * q^82 + 40 * q^83 + 2 * q^84 - 28 * q^86 + 126 * q^88 - 68 * q^89 - 72 * q^91 + 52 * q^92 + 34 * q^94 - 4 * q^97 + 4 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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